Representation Theory Research Articles

Deformations of Pairs of Kleinian Singularities

Abstract Kleinian singularities, that is, the varieties corresponding to the algebras of invariants of Kleinian groups are of fundamental importance for Algebraic geometry, Representation theory, and Singularity theory. The filtered deformations of these algebras of invariants were classified by Brieskorn (the commutative case) and Losev (the general case). To an inclusion of Kleinian groups, there is the corresponding inclusion of algebras of invariants. We classify deformations of these inclusions when the smaller subgroup is normal in the larger.

Food handlers’ lack of knowledge, and misunderstanding of safe food temperatures: An analysis using the theory of social representations

Comprehension is the ability to understand and be familiar with situations and facts. A critical factor causing foodborne diseases is the inadequate temperature during food storage and handling; food handlers often fail to understand this. Therefore, in this study, we investigated how technical language and everyday knowledge operate in the comprehension of safe food temperatures among food handlers in food services. To achieve this, data collection was carried out in two stages. In the first stage, a survey was conducted to 206 food handlers from 14 food service working in the city of São Paulo. Through this survey, we gathered information to characterize the socio-demographic profile of the sample, details about participation in training, and knowledge of technical terms related to safe food temperatures. In the second stage, individuais interviews were conducted on the same day following the questionnaire administration in each food service. A total of 29 interviews were carried out An interview script was developed containing two storylines based on the Fourth Key: “Keep food at safe temperatures,” which is part of the WHO's “Five Keys to Safer Food” manual. Further, the collective subject discourse technique, which is based on the theory of social representations, was employed to analyze each interview and construct a representative collective discourse. Analysis of the results indicated that lack of knowledge about safe food temperatures is mainly a result of the misunderstanding of technical terms. The collective discourses obtained results reinforced that food handlers had diverse and erroneous information about food defrosting, and they exhibited low confidence and clarity about safe food temperatures. Overall, psychological, social, and cultural factors affect the formation of social representations that guide food handlers’ decision-making.

Bit-twiddling hacks for gamma matrices

For some research questions that involve Spin(p, q) representation theory, using symbolic algebra based techniques might be an attractive option for simplifying and manipulating expressions. Yet, for some such problems, especially as they arise in the study of various limits of M-theory (such as dimensional reductions), the complexity of the resulting expressions can become computationally challenging when using popular symbolic algebra packages in a straightforward manner.This work discusses some general properties of Gamma matrices that are computationally useful, down to the level of what one would call “bit-twiddling hacks” in computer science. It is presented in a self-contained way that should be accessible to both physicists and computer scientists. Code is available alongside the TeX source of the preprint version of this article on arXiv.

Realisations of Racah algebras using Jacobi operators and convolution identities

Using the representation theory of sl2 and an appropriate model for tensor product of lowest weight Verma modules, we give a realisation first of the Hahn algebra, and then of the Racah algebra, using Jacobi differential operators. While doing so we recover some known convolution formulas for Jacobi polynomials involving Hahn and Racah polynomials. Similarly, we produce realisations of the higher rank Racah algebras in which maximal commutative subalgebras are realised in terms of Jacobi differential operators.

Yanmiri, Aboki, Afonja: Discursive Construction of Ethnic Others in Nigerian Online Discussion

How are discursive expressions of alterity online constructed? What factors engender this form of discourse and what is the socio-cognitive basis? What are implications of this construction of ethnic otherness online for a multiethnic nation like Nigeria? This study anchors on these questions. These issues were explored based on theories of social representation and discursive discrimination, such as social constructionism, biological determinism, symbolic interactionism. The study analysed the commenting behaviour of Nigerians drawn from Nairaland Forum based on van Dijk’s (1996) social representation theory and Boreus’ (2006) typology of discursive discrimination. The findings revealed that prejudices and stereotypes are premised on experiences and opinions that lead to generalisation, group polarisation illusory correlation, and attribution errors. Negative other presentations are achieved through labelling, deployment of environmentalbased peculiarities, struggles for socio-economic goals, ethnic sociocultural peculiarities, behaviour and appearances as well as perceived personality traits. These issues are accentuated through the deployment of linguistic and discursive forms and strategies, such as the mood system, adjectivisation, metaphorisation, lexicalisation, humorisation, and essentialisation. The study concludes that despite the fact that expressions of alterity are identified as online phenomena, they often impact offline intergroup relations.

Semi-infinite construction for the double Yangian of type [formula omitted

We consider certain infinite dimensional modules of level 1 for the double Yangian DY(gl2) which are based on the Iohara–Kohno realization. We show that they possess topological bases of Feigin–Stoyanovsky-type, i.e. the bases expressed in terms of semi-infinite monomials of certain integrable operators which stabilize and satisfy the difference two condition. Finally, we give some applications of these bases to the representation theory of the corresponding quantum affine vertex algebra.

Representation from Below: How Women’s Grassroots Party Activism Promotes Equal Political Participation

Extensive research investigates the impact of descriptive representation on women’s political participation; yet, the underlying mechanisms remain unclear. This article develops a novel theory of descriptive representation, arguing that women politicians mobilize women’s political participation by recruiting women as grassroots party activists. Evidence from a citizen survey and the natural experiment of gender quotas in India confirm that women politicians are more likely to recruit women party activists, and citizens report greater contact with them in reserved constituencies during elections. Furthermore, with women party activists at the helm, electoral campaigns are more likely to contact women, and activist contact is positively associated with political knowledge and participation. Evidence from representative surveys of politicians and party activists and fieldwork in campaigns, further support the theory. The findings highlight the pivotal role of women’s party activism in shaping women’s political behavior, especially in contexts with pervasive clientelism and persistent gender unequal norms.

Social representations of elderly people about living with HIV/AIDS

Objective: This study aims to understand the social representations of elderly people about living with HIV/AIDS. Methods: This is a cross-sectional study, descriptive-analytical, with a qualitative approach and theoretical and methodological support from the Collective Memory Theory and the Social Representations Theory. Conducted with 38 elderly people. It used a questionnaire with sociodemographic data, health conditions, and a script for a semi-structured interview. The data analysis with the support of the QRS NVivo® Software and in the light of Bardin’s Content Analysis. Results: The social representations of elderly persons, about living with HIV were: ruptures, living with treatment and coping with prejudice and the struggle for (over)living: the fear of dying and the spread of the diagnosis. Conclusion: Social representations of the elderly about living with HIV/AIDS are about living with drug treatment, with the disruptions in their lives, health care, self-care, and pain of social arising from prejudice.

Community Preparedness to Recurrent Flood Disasters in Babessi, Rural Cameroon

Purpose: Flood is a recurrent natural disaster that has caused enormous human and material damage in many places and continues to hit rural communities at an alarming rate. Flood affects the community extensively and it is crucial for them to be prepared to reduce the risk faced in the event of a flood disaster. The need to improve on education, local flood disaster committee, public awareness and early warnings as preparedness measures to prevent and manage flood disasters by rural communities is therefore indispensable. This study aims to determine the current level of flood preparedness amongst households in Babessi, Cameroon as well as other contributing factors to preparedness such as the availability of flood forecast and early warning and public awareness to prepare for floods.
 Methodology: This study used the mixed methods approach that combined descriptive and analytical perspectives. It collected and analyzed both qualitative and quantitative data concurrently and sequentially and integrated data at one or more stages in the process. Using a structured questionnaire, data was purposively and randomly selected from 317 households from the same. Quantitative data were supplemented by 7 key informant interviews and 2 focused group discussions. All quantitative data generated from the questionnaires were entered into a template designed in the Statistical Package for Social Sciences (SPSS version 20). The data were cleaned and later on analyzed using both SPSS and Microsoft Excel 2013. For qualitative data (FGDs and KIIs), they were recorded in the field using Dictaphones (voice recorder) and later on transcribed and typed into a word processing program (Microsoft Word 2013). The transcribed data were analyzed using Nvivo version 11, and themes were established in relation to research objective. Results were presented using tables, figures and charts.
 Findings: Using descriptive analysis, the findings indicated that the preparedness measures were mostly stocking of equipment (sand and sand bags) followed by emergency savings, stocking of emergency relief materials (food, water and drugs). Availability of flood forecast and early warning systems, education and public awareness were low overall preparedness level. The population of Babessi needs heightened sensitization on the impending dangers of flood hazard and be encouraged to participate in implementing the adopted strategies to prevent and manage subsequent flood disasters.
 Recommendations: The Social Representations Theory (SRT) informed this study. A social representation is a system of values, ideas and practices regarding a given social object, as well as the elaboration of that object by a group for the purpose of communicating and behaving. For policy, to enhance information dissemination, investments should be made in improving communication infrastructure and disseminating timely and accurate information about flood risks, early warnings, evacuation procedures, and available support services.

Associative algebras and the representation theory of grading-restricted vertex algebras

We introduce an associative algebra [Formula: see text] using infinite matrices with entries in a grading-restricted vertex algebra [Formula: see text] such that the associated graded space [Formula: see text] of a filtration of a lower-bounded generalized [Formula: see text]-module [Formula: see text] is an [Formula: see text]-module satisfying additional properties (called a nondegenerate graded [Formula: see text]-module). We prove that a lower-bounded generalized [Formula: see text]-module [Formula: see text] is irreducible or completely reducible if and only if the nondegenerate graded [Formula: see text]-module [Formula: see text] is irreducible or completely reducible, respectively. We also prove that the set of equivalence classes of the lower-bounded generalized [Formula: see text]-modules is in bijection with the set of the equivalence classes of nondegenerate graded [Formula: see text]-modules. For [Formula: see text], there is a subalgebra [Formula: see text] of [Formula: see text] such that the subspace [Formula: see text] of [Formula: see text] is an [Formula: see text]-module satisfying additional properties (called a nondegenerate graded [Formula: see text]-module). We prove that [Formula: see text] are finite-dimensional when [Formula: see text] is of positive energy (CFT type) and [Formula: see text]-cofinite. We prove that the set of the equivalence classes of lower-bounded generalized [Formula: see text]-modules is in bijection with the set of the equivalence classes of nondegenerate graded [Formula: see text]-modules. In the case that [Formula: see text] is a Möbius vertex algebra and the differences between the real parts of the lowest weights of the irreducible lower-bounded generalized [Formula: see text]-modules are less than or equal to [Formula: see text], we prove that a lower-bounded generalized [Formula: see text]-module [Formula: see text] of finite length is irreducible or completely reducible if and only if the nondegenerate graded [Formula: see text]-module [Formula: see text] is irreducible or completely reducible, respectively.

Representation Theory of Quivers and Finite-Dimensional Algebras

Representation Theory of Quivers and Finite-Dimensional Algebras

Degenerate Perturbation Theory for Models of Quantum Field Theory with Symmetries

We consider Hamiltonians of models describing non-relativistic quantum mechanical matter coupled to a relativistic field of bosons. If the free Hamiltonian has an eigenvalue, we show that this eigenvalue persists also for nonzero coupling. The eigenvalue of the free Hamiltonian may be degenerate provided there exists a symmetry group acting irreducibly on the eigenspace. Furthermore, if the Hamiltonian depends analytically on external parameters then so does the eigenvalue and eigenvector. Our result applies to the ground state as well as resonance states. For our results, we assume a mild infrared condition. The proof is based on operator theoretic renormalization. It generalizes the method used in Griesemer and Hasler (Ann Henri Poincaré 10(3):577–621, 2009) to non-degenerate situations, where the degeneracy is protected by a symmetry group, and utilizes Schur’s lemma from representation theory.

Elucidating protein-ligand binding kinetics based on returning probability theory.

The returning probability (RP) theory, a rigorous diffusion-influenced reaction theory, enables us to analyze the binding process systematically in terms of thermodynamics and kinetics using molecular dynamics (MD) simulations. Recently, the theory was extended to atomistically describe binding processes by adopting the host-guest interaction energy as the reaction coordinate. The binding rate constants can be estimated by computing the thermodynamic and kinetic properties of the reactive state existing in the binding processes. Here, we propose a methodology based on the RP theory in conjunction with the energy representation theory of solution, applicable to complex binding phenomena, such as protein-ligand binding. The derived scheme of calculating the equilibrium constant between the reactive and dissociate states, required in the RP theory, can be used for arbitrary types of reactive states. We apply the present method to the bindings of small fragment molecules [4-hydroxy-2-butanone (BUT) and methyl methylthiomethyl sulphoxide (DSS)] to FK506 binding protein (FKBP) in an aqueous solution. Estimated binding rate constants are consistent with those obtained from long-timescale MD simulations. Furthermore, by decomposing the rate constants to the thermodynamic and kinetic contributions, we clarify that the higher thermodynamic stability of the reactive state for DSS causes the faster binding kinetics compared with BUT.

An affective reading on narrative productions methodology. Narrative as a body

ABSTRACT From an affective perspective, this work discusses how a Narrative (N), which results from the narrative production methodologies (NPM), can be considered a body. We briefly explain what NPM is, its proceeding, and the theoretical discussion supporting it. Later we present Affect Studies (AS) and their perspective on the body. We propose not to define the body in terms of essence (what is a body) but of capabilities (what can a body do). This proposal leads us to the analysis of the Narrative, considered as a body, based on three concepts: Passage of Affect, Assemblage, and Prehension. The study of narratives has much to offer us if we expand and transcend the limits of representation and embrace theories such as Affect Studies and Posthumanism. This is an invitation not to systematize but to play methodologically with contemporary theoretical points of view and other concepts not considered when NPM was conceived.

Novel finite difference approach to discretize the symplectic dirac operator

Symplectic Dirac operator is an intertwining differential operator. Discretising symplectic Dirac operator gives a new direction to study the quantum space. The construction of discrete symplectic Dirac operator requires the theory of discrete symplectic Clifford analysis or the concept of discrete symplectic connections, which are not explained in literature. In this work, a discretization approach for symplectic Dirac operator is suggested by considering the forward and backward basis vectors on symplectic Clifford algebra. The suggested discrete symplectic Dirac operator is Ds=Ds++Ds- where the Ds+ and Ds- are the forward and backward discrete symplectic Dirac operators, respectively. The new discrete symplectic Dirac operator gives the factorization of discrete Laplacian on symplectic spaces. Further, we establish commutation relations involving forward and backward discrete symplectic Dirac operators in the representation theory.

Chance-Constrained Joint Dispatch of Generation and Wind Curtailment-Load Shedding Schemes With Large-Scale Wind Power Integration

Wind curtailment (WC) and load shedding (LS) are indispensable measures to mitigate the operational risk in high-renewable power systems. Moreover, WC and LS schemes should be pre-scheduled and confirmed by related entities to make them applicable. In this paper, we propose a novel chance-constrained economic dispatch (CCED) model which can generate optimal WC and LS schemes accounting for the reserve shortage and transmission congestion problems. In the proposed method, WC and LS power are formulated as random decision variables, with which the infeasibility issues of conventional CCED are fully addressed. To solve the proposed model, we first convert the complicated chance constraints into a set of deterministic inequalities equivalently by employing the conditional Value-at-Risk (CVaR) representation and duality theory. Then, a two-layer iterative algorithm is proposed to solve the equivalent problem efficiently, which is based on the generalized Benders decomposition (GBD) framework. Numerical tests demonstrate the effectiveness and efficiency of the proposed method.

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.

The identity‐attitude nexus in the representation of energy transition in a coal region (Sulcis, Italy): An exploration through the Structural Topic Model

AbstractThis article explores the contribution of the Structural Topic Model (STM) to study the intertwining of social representations, attitudes, and identities. We examine newspapers’ discourse on energy transition in a coal‐dependent region (Sulcis, Italy), whose identity and economy are built around mining and carbon‐intensive industry. Drawing upon Social Representations Theory, we combined STM and qualitative content analysis to examine how newspapers represented the energy issue in Sulcis, and how these representations (including denotative and connotative facets) differed according to the social identities’ salience. Results show that coal is legitimated by discourses making salient local identities and providing continuity in the place–identity link, with no alternative to extractivism. When the Sardinian superordinate identity becomes salient, new themes emerge (e.g., renewables) but energy transition retains ambivalent or negative connotations. Overall representations seem to replicate and reflect processes of domination and injustice hindering a just transition, potentially explaining negative attitudes and collective resistance to decarbonization.

The paradox of Portuguese /Vr/-rhymes: Disentangling weight from length via structure-based sonority

The assumption that Portuguese stress is weight-sensitive is supported by strong arguments. However, oxytones ending with open syllables remain a major problem for this claim, unless vowels can be independently proved to be heavy without being long. It will be seen how the behaviour of /Vr/-rhymes in European Portuguese, which is not satisfactorily accounted for by standard models, shows that weight and length are distinct aspects, and solves the problem of oxytones. The price to be paid is a theory of phonological representations in which sonority is based on structure, not on features.

Mackey's obstruction map for discrete graded algebras

G.W. Mackey's celebrated obstruction theory for projective representations of locally compact groups was remarkably generalized by J. M. G. Fell and R. S. Doran to the wide area of saturated Banach *-algebraic bundles.Analogous obstruction is suggested here for discrete group graded algebras which are not necessarily saturated, i.e. strongly graded in the discrete context. The discrete obstruction is a map assigning a certain second cohomology class to every equivariance class of absolutely graded-simple modules.The set of equivariance classes of such modules is equipped with an appropriate multiplication, namely a graded product, such that the obstruction map is a homomorphism of abelian monoids. Graded products, essentially arising as pull-backs of bundles, admit many nice properties, including a way to twist graded algebras and their graded modules.The obstruction class turns out to determine the fine part that appears in the Bahturin-Zaicev-Sehgal decomposition, i.e. the graded Artin-Wedderburn theorem for graded-simple algebras which are graded Artinian, in case where the base algebras (i.e. the unit fiber algebras) are finite-dimensional over algebraically closed fields.