Representation Theory Research Articles

Studying social representations of cross-boundary collaboration between managers through drawings

This study examines cross-boundary collaboration between middle managers working in health and social care in Finland. It approaches the topic from social representations theory, focusing on middle managers’ everyday perceptions and experiences of cross-boundary collaboration. Drawing images of collaboration was used as an arts-based method of data production. The data consisted of 14 drawings (one from each participating manager) depicting collaboration between managers and their verbal reflections. The visual and verbal data were analyzed by content analysis. The study identified four social representations of collaboration between managers: feeling of togetherness, challenge of dispersion, reward of practicality, and joys and sorrows of diversity. The paper contributes to the current knowledge on cross-boundary collaboration between managers with practical implications. In addition, the paper provides a novel theoretical and methodological approach to studying cross-boundary collaboration.

THE REPRESENTATION OF BULLYING IN AMERICAN FILMS

The issue of bullying continues to be reported by the media because it still happens everywhere, especially in schools, and needs to be discussed in research. This qualitative research focuses on studying American films with the theme of bullying, namely Bully (2011), A Girl Like Her (2015), and Wonder (2017) as the main source of data. This study aims to identify how American movies portray bullying and to find out what bullying represents by applying Hall’s representation theory. Dialogs collected and sorted from the films were treated as signs that would convey more meanings. The results of data analysis suggest that American films with the themes of bullying frequently show bullying through portraits of physical violence, verbal violence, and trauma. Besides, bullying can also indicate a lack of attention from the family, the condition of the social environment, and the powerlessness of humans.

New structure on the quantum alcove model with applications to representation theory and Schubert calculus

The quantum alcove model associated to a dominant weight plays an important role in many branches of mathematics, such as combinatorial representation theory, the theory of Macdonald polynomials, and Schubert calculus. For a dominant weight, it is proved by Lenart–Lubovsky that the quantum alcove model does not depend on the choice of a reduced alcove path, which is a shortest path of alcoves from the fundamental one to its translation by the given dominant weight. This is established through quantum Yang–Baxter moves, which biject the objects of the models associated to two such alcove paths, and can be viewed as a generalization of jeu de taquin slides to arbitrary root systems. The purpose of this paper is to give a generalization of quantum Yang–Baxter moves to the quantum alcove model corresponding to an arbitrary weight, which was used to express a general Chevalley formula for the equivariant K -group of semi-infinite flag manifolds. The generalized quantum Yang–Baxter moves give rise to a “sijection” (bijection between signed sets), and are shown to preserve certain important statistics, including weights and heights. As an application, we prove that the generating function of these statistics does not depend on the choice of a reduced alcove path. Also, we obtain an identity for the graded characters of Demazure submodules of level-zero extremal weight modules over a quantum affine algebra, which can be thought of as a representation-theoretic analogue of the mentioned Chevalley formula.

Exotic C⁎-algebras of geometric groups

We consider a new class of potentially exotic group C*-algebras C⁎(PFp⁎(G)) for a locally compact group G, and its connection with the class of potentially exotic group C*-algebras CLp⁎(G) introduced by Brown and Guentner. Surprisingly, these two classes of C*-algebras are intimately related. By exploiting this connection, we show CLp⁎(G)=C⁎(PFp⁎(G)) for p∈(2,∞), and the C*-algebras CLp⁎(G) are pairwise distinct for p∈(2,∞) when G belongs to a large class of nonamenable groups possessing the Haagerup property and either the rapid decay property or Kunze-Stein phenomenon by characterizing the positive definite functions that extend to positive linear functionals of CLp⁎(G) and C⁎(PFp⁎(G)). This greatly generalizes earlier results of Okayasu (see [30]) and the second author (see [40]) on the pairwise distinctness of CLp⁎(G) for 2<p<∞ when G is either a noncommutative free group or the group SL(2,R), respectively.As a byproduct of our techniques, we present two applications to the theory of unitary representations of a locally compact group G. Firstly, we give a short proof of the well-known Cowling-Haagerup-Howe Theorem, which presents sufficient condition implying the weak containment of a cyclic unitary representation of G in the left regular representation of G (see [14]). Also we give a near solution to a 1978 conjecture of Cowling stated in [10]. This conjecture of Cowling states if G is a Kunze-Stein group and π is a unitary representation of G with cyclic vector ξ such that the mapG∋s↦〈π(s)ξ,ξ〉 belongs to Lp(G) for some 2<p<∞, then Aπ⊆Lp(G). We show Bπ⊆Lp+ϵ(G) for every ϵ>0 (recall Aπ⊆Bπ).

The integrality of distance spectra of quasiabelian 2-Cayley graphs

A graph Γ is called an n-Cayley graph over a group G if there exists a semiregular subgroup of Aut(Γ) isomorphic to G with n orbits. In this paper, we first establish a decomposition formula for the distance spectra of n-Cayley graphs over arbitrary finite groups by using the lifted graphs, the matrix theory and the group representation theory. Secondly, we completely determine the distance splitting fields and the distance algebraic degrees of quasiabelian 2-Cayley graphs. Finally, we present some criteria for the distance integrality of quasiabelian 2-Cayley graphs. Moreover, we present some sufficient conditions for the equivalence between the integrality and the distance integrality of 2-Cayley graphs over abelian groups. We also give some sufficient conditions for the integrality of distance powers of 2-Cayley graphs over abelian groups. Our results generalize several previously known results.

Electoral Legitimacy and Gender Representation Barriers; Theories and Practices in Nigeria

The article describes relevant concepts and theories on Gender Representation and Electoral Legitimacy behaviours and barriers that obstruct global policies for gender equity model to a free and fair election. The limiting barriers and theories described, include Class-Conflict versus Representation Theory, Gender vs Culture, Electoral Legitimacy Deficit vs Dominance Theory, Machismo Culture, Institutional concept, Human Capital, Feminist Rights Concepts (FGF) and the UN Think, Assess, Consider, and Take Action (UNTACT) Concept. The article adopts a descriptive secondary qualitative method to gather data on the key theories, barriers and practices affecting gender representation electoral. Data collection include previous studies, articles, reports, publications, and Electoral Commission official documents already generated. These various sources of information gathered, was critically examined, reviewed, analysed, and synthesized to understand the context in which gender representation barriers exist. Research results indicted Nigeria Electoral process as extremely unreliable at the output-delivery process, and thus, criticised for having flaws and failing to completely enforce candidate electoral rules, which impacts female representation. However, the research contributed to a deeper understanding of the complexities surrounding electoral theories, practices and their impact on electoral system’s legitimacy. Findings suggest, importance of challenging patriarchal electioneering structures, cultural norms, and power imbalances in the political sphere and the need for power dynamics to be examined critically, to deliver effective gender or female representation. Keywords: Electoral Legitimacy, Gender Representation, Theories, Barriers, Nigeria.

Theatre-for-Development as Information Panacea for Rural Dwellers in Nigeria during a Pandemic: Lessons from COVID-19

The subject of COVID-19 (coronavirus) in Nigeria emerged with various misrepresentations and conspiracy theories, such as the notion of COVID-19 as a forerunner of the Anti-Christ or the commencement of a 'New World Order' occasioned by the 5G network. COVID-19 information in Nigeria was managed by the Presidential Task Force through daily media briefings. This paper examined the PTF's information dissemination structure and its impact on four indigenous communities in south-eastern Nigeria: Ikwo in Ebonyi State, Iva-Valley Forestry Hill Camp 1 in Enugu State, Umualumu Old Road in Imo State, and Ogbagu Obukpa in Enugu State. TfD was used during lockdown to inform indigenous communities and promote necessary health precautions. The project used TfD and Brecht's Epic Theatre Theory in 4 Nigerian communities to show how TfD can complement other media in informing rural residents about COVID-19. TfD mobilized indigenous communities in southeastern Nigeria to understand Igbo and take COVID-19 precautions despite PTF's robust information dissemination structure. TfD could have helped the PTF share vital COVID-19 info with rural communities in Nigeria. The Nigerian government should establish a robust infrastructure for raising awareness and combating COVID-19 and other pandemics in rural areas through TfD

Some two-weight codes invariant under the 3-fold covers of the Mathieu groups M22 and Aut(M22)

Using an approach from finite group representation theory we construct quaternary non-projective codes with parameters [Formula: see text], quaternary projective codes with parameters [Formula: see text] and [Formula: see text] and binary projective codes with parameters [Formula: see text] as examples of two-weight codes on which a finite almost quasisimple group of sporadic type acts transitively as permutation groups of automorphisms. In particular, we show that these codes are invariant under the [Formula: see text]-fold covers [Formula: see text] and [Formula: see text], respectively, of the Mathieu groups [Formula: see text] and [Formula: see text]. Employing a known construction of strongly regular graphs from projective two-weight codes we obtain from the binary projective (respectively, quaternary projective) two-weight codes with parameters those given above, the strongly regular graphs with parameters [Formula: see text] and [Formula: see text] respectively. The latter graph can be viewed as a [Formula: see text]-[Formula: see text]-symmetric design with the symmetric difference property whose residual and derived designs with respect to a block give rise to binary self-complementary codes meeting the Grey–Rankin bound with equality.

Process of constructing alternative social work discourses in Asia: A case study of Buddhist social work as social representations

AbstractThis preliminary study examined the process of constructing alternative discourses on social work. It focused on the exploration of Buddhist social work by researchers and practitioners in Asian countries, including monks and nuns. The present investigation was grounded in the analytical perspective of the social representation theory posited in the domain of social psychology. Books, reports, and any relevant papers written in English were collected as primary data sources (n = 22), and a qualitatively descriptive analysis was conducted on these data. The scrutiny specifically attended to the mechanism of familiarization, which comprises the process of anchoring and objectifying. The study's findings revealed the process of intentionally (re)naming activities and related events that were previously not necessarily described as Buddhist social work. These practices and occurrences were then classified and positioned within a particular cross‐border paradigm. Additionally, some monks, nuns, and other stakeholders became conversant with discussion and research activities related to Buddhist social work. Objectifying actions, such as (re)discovering and reproducing, thus became taken for granted by such functionaries. These findings suggest that cross‐border Buddhist social work discourses were actively constructed through the usage of relevant terms and concepts. In other words, the results of this study indicate that alternative discourse is internationally becoming the familiar form of discussion within the discipline.

Hitchin representations of Fuchsian groups

We survey the theory of Hitchin representations of closed surface groups into \mathsf{PSL}(d,\mathbb R) with a focus on their dynamical and geometric properties. We then describe recent extensions of this work to study Hitchin representations of co-finite area Fuchsian groups. The motivation for this recent work is a conjecture about the geometry of the augmented Hitchin component.

Partisan science and the democratic legitimacy ideal

The democratic legitimacy ideal requires value judgments in science to be legitimised by democratic procedures in order for them to reflect the public interest or democratic aims. Such a view has been explicitly defended by Intemann (2015) and Schroeder (2021), amongst others, and reflects a more widely shared commitment to a democratisation of science and integration of public participation procedures. This paper suggests that the democratic legitimacy ideal in its current form does not leave space for partisan science – science that is politically or societally engaged. This is problematic because partisan research can contribute substantially to science and society, a point that I will illustrate with a recent case study from the Netherlands. To resolve this problem, I scrutinise the notion of democratic legitimacy and consider its use in the values in science discourse. Current discussions focus on democratic decision-making procedures to legitimise specific value judgements. I show that this focus does not adequately represent sound procedures of legitimisation at the hand of political theories of representation. Consequently, I develop a different approach: I propose to consider scientists as a special case of representatives who are authorised to make independent value judgements while nevertheless being constrained by the demands of their constituencies. Based on this approach, I argue that values in science do not need to be based on democratically agreed upon aims or the public interest in every instance. Instead, I advocate for a pluralist system of scientific mandates, which differs from both value pluralism and the democratic legitimacy ideal.

Computational aspects of Calogero–Moser spaces

We present a series of algorithms for computing geometric and representation-theoretic invariants of Calogero–Moser spaces and rational Cherednik algebras associated with complex reflection groups. In particular, we are concerned with Calogero–Moser families (which correspond to the mathbb {C}^times -fixed points of the Calogero–Moser space) and cellular characters (a proposed generalization by Rouquier and the first author of Lusztig’s constructible characters based on a Galois covering of the Calogero–Moser space). To compute the former, we devised an algorithm for determining generators of the center of the rational Cherednik algebra (this algorithm has several further applications), and to compute the latter we developed an algorithmic approach to the construction of cellular characters via Gaudin operators. We have implemented all our algorithms in the Cherednik Algebra Magma Package by the second author and used this to confirm open conjectures in several new cases. As an interesting application in birational geometry we are able to determine for many exceptional complex reflection groups the chamber decomposition of the movable cone of a mathbb {Q}-factorial terminalization (and thus the number of non-isomorphic relative minimal models) of the associated symplectic singularity. Making possible these computations was also a source of inspiration for the first author to propose several conjectures about the geometry of Calogero–Moser spaces (cohomology, fixed points, symplectic leaves), often in relation with the representation theory of finite reductive groups.

The integrality conjecture and the cohomology of preprojective stacks

Abstract We study the Borel–Moore homology of stacks of representations of preprojective algebras Π Q \Pi_{Q} , via the study of the DT theory of the undeformed 3-Calabi–Yau completion Π Q ⁢ [ x ] \Pi_{Q}[x] . Via a result on the supports of the BPS sheaves for Π Q ⁢ [ x ] ⁢ -mod \Pi_{Q}[x]\textup{-mod} , we prove purity of the BPS cohomology for the stack of Π Q ⁢ [ x ] \Pi_{Q}[x] -modules and define BPS sheaves for stacks of Π Q \Pi_{Q} -modules. These are mixed Hodge modules on the coarse moduli space of Π Q \Pi_{Q} -modules that control the Borel–Moore homology and geometric representation theory associated to these stacks. We show that the hypercohomology of these objects is pure and thus that the Borel–Moore homology of stacks of Π Q \Pi_{Q} -modules is also pure. We transport the cohomological wall-crossing and integrality theorems from DT theory to the category of Π Q \Pi_{Q} -modules. We use our results to prove positivity of a number of “restricted” Kac polynomials, determine the critical cohomology of Hilb n ⁡ ( A 3 ) \operatorname{Hilb}_{n}(\mathbb{A}^{3}) , and the Borel–Moore homology of genus one character stacks, as well as providing various applications to the cohomological Hall algebras associated to Borel–Moore homology of stacks of modules over preprojective algebras, including the PBW theorem, and torsion-freeness.

The Conventionality of Real-Valued Quantities

AbstractThe original architects of the representational theory of measurement interpreted their formalism operationally and explicitly acknowledged that some aspects of their representations are conventional. We argue that the conventional elements of the representations afforded by the theory require careful scrutiny as one moves toward a more metaphysically robust interpretation by showing that there is a sense in which the very number system one uses to represent a physical quantity such as mass or length is conventional. This result undermines inferences which impute structure from the numerical representational structure to the quantity it is used to represent.

Use of Social Representation to Validate the Structural Equations Modelling

This article proposes the use of social representation theory to validate the structural model of structural equation modeling and better understand the research object. For this purpose, action research was used to construct, implement, and confirm the practical feasibility of adopting the methodological procedures described in this article, based on their practical application in an analysis case. We concluded that it was possible to validate the structural model used in structural equation modeling, using the proposed methodological procedures, applied to a case involving the governance system construct. This opens up the possibility of its future use in other research, which use structural equation modeling to validate a theoretical model and the causal relationships between its constructs. As such, we reduce the risk of using this statistical method to validate a theoretical model whose causal relationships do not represent a reality supported by practice, going beyond theoretical validation.

Neo-Exoticism Discourses in Indonesian Online Media: Normalizing Cultural Tourism Regime amid Market Economy

This article explores the construction of neo-exoticism discourses in Indonesian online news media. Drawing on online news media research, we show how the transformation of ethnic cultures in Banyuwangi, East Java, Indonesia were positioned as the basis of various tourism events using the representation theory with the discursive constructionist approach. We focus on how some Indonesian online news media reported and positioned Banyuwangi Festival through quotations of government’s official’s statements and descriptions of cultural events that emphasize the transformation of ethnic cultures to meet national and global tourism markets. In doing so, Indonesian online news media actively produced, promoted, and distributed discourses of neo exoticism by emphasizing the beauty of certain of traditional rites, fashions, and arts in various carnivals and festivals. In addition, the media constructed neo-exoticism discourses as a formulas to popularize cultural and touristic events which proved to be beneficial, economically, for local people. However, we argue that broadcasting neo-exotic narratives also created online news media discursive subjects that normalize tourism regimes as managed by the cooperation of government and investors.

Facing up to the problem of intentionality

AbstractWe distinguish between different problems of “aboutness”: the “hard” problem of explaining the everyday phenomenon of intentionality and three less challenging “easy” sets of problems concerning the posits of folk psychology, the notions of representation invoked in the mind‐brain sciences, and the intensionality (with an “s”) of mental language. The problem of intentionality is especially hard in that, as is the case with the hard problem of phenomenal consciousness, there is no clear path to a solution using current methods. We argue that naturalistic theories of mental representation do not address the hard problem—either they are only intended to address the easy problems, or the claims they make help address the problem of intentionality only under undefended and prima facie implausible assumptions to the effect that the hard problem reduces to some combination of the easy problems. We offer a positive account of what would be required to properly face up to the problem of intentionality.

The COVID-19 Pandemic and the Digital Transformation of Workplace: The Social Representation of Home-Office

In March 2020, with the World Health Organization declaring COVID-19 a pandemic and prescribing social isolation to combat this coronavirus, companies began to implement home-office, with employees working from their homes through Information and Communication Technology. Thus, this study aims to identify how Human Resources professionals in Brazil made sense of the home-office policy adopted by their companies during the COVID-19 pandemic, given that this country was severely impacted by this disease, which led to the implementation of social isolation for several months. In consideration of this, this research applied the Social Representation Theory, operationalized via the evocation of words technique and implicative analysis. In doing so, a positive and less comprehensive view of Human Resources professionals was identified vis-à-vis the academic literature in relation to the enactment of home-office via companies during the COVID-19 pandemic, which may be due to the time interval in which this research was carried out, the consequent impacts resulting from the implementation of the home-office at the time of data collection, and the very fact that most of the literature researched came from developed countries and not from the Global South where this research was carried out. Flexibility and Quality of Life were the dimensions most associated with the social representation of home-office according to Human Resources professionals. However, the productivity dimension related to working in a home-office showed dubious and inconclusive results. Finally, some challenging aspects related to this model of work raised by the scientific literature were not mentioned by the respondents, indicating a mismatch between the academic literature and the understanding of Human Resources professionals about the role of home-office during the COVID-19 pandemic.

The partial Temperley–Lieb algebra and its representations

In this paper, we give a combinatorial description of a new diagram algebra, the partial Temperley–Lieb algebra, arising as the generic centralizer algebra \mathrm{End}_{\mathbf{U}_q(\mathfrak{gl}_2)}(V^{\otimes k}) , where {V = V(0) \oplus V(1)} is the direct sum of the trivial and natural module for the quantized enveloping algebra \mathbf{U}_q(\mathfrak{gl}_2) . It is a proper subalgebra of the Motzkin algebra (the \mathbf{U}_q(\mathfrak{sl}_2) -centralizer) of Benkart and Halverson. We prove a version of Schur–Weyl duality for the new algebras, and describe their generic representation theory.

Modular representations of finite groups and Lie theory

This article discusses the modular representation theory of finite groups of Lie type from the viewpoint of Broué's abelian defect group conjecture. We discuss both the defining characteristic case, the inspiration for Alperin's weight conjecture, and the non-defining case, the inspiration for Broué's conjecture. The modular representation theory of general finite groups is conjectured to behave both like that of finite groups of Lie type in defining characteristic, and in non-defining characteristic, to a large extent.The expected behavior of modular representation theory of finite groups of Lie type in defining characteristic is particularly difficult to grasp along the lines of Broué's conjecture, and we raise a new question related to the change of central character.We introduce a degeneration method in the modular representation theory of finite groups of Lie type in non-defining characteristic. Combined with the rigidity property of perverse equivalences, this provides a setting for two-variable decomposition matrices, for large characteristic. This should help make progress towards finding decomposition matrices, an outstanding problem with few general results beyond the case of general linear groups. This last part is based on joint work with David Craven and Olivier Dudas.