Representation Theory Research Articles

Representations of free products of semisimple algebras via quivers

We use quiver representation theory and King's notion of stable representations to study the (finite dimensional) representations of free products of semi-simple associative K-algebras over an algebraically closed field K. We obtain numerical criteria giving necessary conditions for a module over such a free product to be simple and prove that these conditions are sufficient for modules in general position. We also prove that modules in general position are always semisimple, although non-semisimple modules always exist when the algebra is infinite dimensional. With essentially a single exception, all module categories are strictly wild; moreover these categories admit no bounds on the dimensions of simple modules. We use quiver moduli spaces to derive a closed formula for the number of parameters needed to describe all simple modules in a given dimension. As a special case, we apply our results to free products of finite groups, and recover the representation theory of the projective modular group PSL2(Z) (strictly wild) and of the infinite dihedral group (tame).

On functors preserving projective resolutions

It is important for applications of Homological Algebra in Representation Theory to have control over the behavior of (minimal) projective resolutions under various functors. In this paper, we describe three broad families of functors that preserve such resolutions. We will use these results in our work on Representation Theory of Schur algebras.

Development of the Method of Averaging in Clifford Geometric Algebras

We develop the method of averaging in Clifford (geometric) algebras suggested by the author in previous papers. We consider operators constructed using two different sets of anticommuting elements of real or complexified Clifford algebras. These operators generalize Reynolds operators from the representation theory of finite groups. We prove a number of new properties of these operators. Using the generalized Reynolds operators, we give a complete proof of the generalization of Pauli’s theorem to the case of Clifford algebras of arbitrary dimension. The results can be used in geometry, physics, engineering, computer science, and other applications.

Representasi Waria dalam Sinema Indonesia pada Masa Orde Baru Sampai Era Moral Panic

The banning of transgender representation in the mainstream media by KPI has limit the way society is empowered on the issues concerning transgender in Indonesia. The development of transgender representation in the media are not as progressive as it could be without the banning from KPI. This research aims to investigate Betty Bencong Slebor (1978), Dulu Banci (2011), Aku Bukan Banci Kaleng (2012), Bias (2015), and On Friday Noon (2016) films in reference to representation theory to compare and contrast on how waria is represented during the New Order , post-reformation, and moral panic eras. Research findings reveal that films produced during the post-reformation period tend to perpetuate the stereotype of waria as it was constructed during the New Order era because of the government's refusal to classify waria as women. Furthermore, waria are often represented in the context of religious, spesifically Islamic, values. During the moral panic era, several stereotypes have actually been contested in the films even though stereotypes regarding waria’s appearance and job are still strongly discriminating. 
 Keywords: identity; Indonesia cinema; KPI; representation; waria

An Effective Near-Field to Far-Field Transformation with Planar Spiral Scanning for Flat Antennas under Test.

The goal of this article is to provide numerical and experimental assessments of an effective near-field to far-field transformation (NF-FF T) technique with planar spiral scanning for flat antennas under test (AUTs), which requires a non-redundant, i.e., minimum, number of NF measurements. This technique has its roots in the theory of non-redundant sampling representations of electromagnetic fields and was devised by suitably applying the unified theory of spiral scans for non-volumetric antennas to the case in which the considered AUT is modeled by a circular disk having its radius equal to half of the AUT's maximum dimension. It makes use of a 2D optimal sampling interpolation (OSI) formula to accurately determine the massive amount of NF data required by the classical plane-rectangular NF-FF T technique from the non-redundant data gathered along the spiral. It must be emphasized that, when considering flat AUTs, the developed transformation allows one to further and significantly save measurement time as compared to that required by the previously developed NF-FF T techniques with planar spiral scans based on a quasi-planar antenna modeling, because the number of turns of the spiral and that of NF data to be acquired depend somewhat on the area of the modeling surface. The reported numerical simulations assess the accuracy of the proposed NF-FF T technique, whereas the experimental tests prove its practical feasibility.

Matrix factorizations, Reality and Knörrer periodicity

AbstractMotivated by periodicity theorems for Real ‐theory and Grothendieck–Witt theory and, separately, work of Hori and Walcher on the physics of Landau–Ginzburg orientifolds, we introduce and study categories of Real matrix factorizations. Our main results are generalizations of Knörrer periodicity to categories of Real matrix factorizations. These generalizations are structurally similar to (1,1)‐periodicity for ‐theory and 4‐periodicity for Grothendieck–Witt theory. We use techniques from Real categorical representation theory, which allow us to incorporate into our main results equivariance for a finite group and discrete torsion twists.

Special Issue: CIMPA Floripa: from dynamics to algebra and representation theory and back

Special Issue: CIMPA Floripa: from dynamics to algebra and representation theory and back

Submerged Economies in Colombia and their Link to Social Representations of Work. A Study from the Perspective of Social Psychology

This reflection article aims at exploring the bases of the historical construction of work in Colombia, its social representations, and its incidence on the constitution of submerged economies such as illegal drug trafficking. The historical method of consulting secondary sources that testify to the behavior of Colombian society at the end of the Colony and in the Republican period is used in order to connect the historical scenarios with the present. Reference is made to the path of dependence, the critical theory of colonialism and social representations of work. The results show that social psychology and social representations of work have consequences in the creation and maturation of informal economies and in the tendency to get rich quickly and easily in some sectors of the Colombian society. In conclusion, these contexts end up being consolidated as the basis of an illegal ‘industry’ that constantly reinvents itself and gives rise to the development of certain skills useful to survive in an unequal and violent context materialized in the so-called drug trafficking era, which began in the 1970s.

Sociomateriality, agential realism, and the metaphysics of accounting information systems: A response to Vosselman and De Loo

I respond to Vosselman and De Loo’s (2023) critique of my earlier paper on agential realism, representation theory, and accounting information systems (Weber, 2020). In that paper, I argued that little is learned by using an agential realism lens to study accounting-related phenomena. I claimed that insights revealed using agential realism also could have been revealed through using existing lenses such as actor-network theory and general systems theory. In particular, I defended representation theory as a way of studying accounting information systems and representationalism as a way of studying the world. Contrariwise, Vosselman and De Loo argue that representation theory and representationalism are useful only in some respects when studying accounting-related phenomena. They contend that agential realism and sociomateriality lenses are needed if the entangled nature of phenomena in accounting domains is to be understood. They point to some assumptions that they claim underpin representationalism and representation theory—assumptions that inhibit their usefulness as a way of studying entangled phenomena. In this response, I present counter-arguments to their claims and defend representationalism and representation theory as ways of understanding the world.

Role of Affective Factors and Concreteness on the Processing of Idioms.

In this study, we asked how the emotional status, i.e., valence and arousal, and concreteness of idioms contribute to their processing. Additionally, we asked whether the contribution of emotional factors and concreteness is modulated by other linguistic constraints, specifically idiom familiarity and decomposability, that has been shown to impact idiom processing. Participants read short idiomatic phrases (e.g., he kicked the bucket), word-by-word and for comprehension while their reaction time was recorded. The results showed that the emotional status of idioms contribute to their processing and this contribution is modulated by familiarity and decomposability levels of idioms in different ways. In particular, the impact of valence (i.e., the degree an idiom is pleasant/unpleasant) was modulated by familiarity, and the impact of arousal was modulated by decomposability. We did not find strong evidence for the contribution of concreteness for idiom processing. Our findings are aligned with theories of semantic representation, which suggest that besides linguistic information, sensory-motor and affective information are fundamental in representing meaning.

Social Representations of Trans People in the Workplace

Organizations show tendencies to discriminate against trans people, making them significantly more likely to face barriers in the professional context, where the highest rates of discrimination against trans people are reported. This study intends to acknowledge the SRs that are associated with trans people in the workplace since the Theory of Social Representations suggests that Social Representations (SRs) are useful to regulate perceptions and the way we act in the world. Also, through Intergroup Contact Theory, by suggesting that contact with a minority population will reduce the associated prejudice, we also intend to understand the impact contact has on SRs. By applying a questionnaire between 20 January and 21 February 2022 on a random sample of 217 people, and respective analyses in MAXQDA 2022 and EVOC 2005 software, the results indicate that the SRs most associated with trans people in a professional context are discrimination, normality, equality, difficulties, and prejudice. Although the term “discrimination” was the most mentioned, it is worth underlining the appearance of positive (and neutral) terms, which may, according to Intergroup Contact Theory, be justified by contact since the majority of the sample (57.6%, n = 125) have had contact with trans people.

Meaning in hand: Investigating shared mechanisms of motor imagery and sensorimotor simulation in language processing

There is substantial evidence to support grounded theories of semantic representation, however the mechanisms of simulation in most theories are underspecified. In the present study, we used an individual differences approach to test whether motor imagery may share some mechanisms with sensorimotor simulations engaged during semantic processing. We quantified individual differences in motor imagery ability via implicit imagery tasks and explicit imagery questionnaires and tested their relationship to sensorimotor effects in syntactic classification tasks. In Experiment 1 (N = 185) we tested relationships between motor imagery and semantic processing of body-object interaction meaning (BOI; the degree to which you can interact with a word's referent) and foot/leg action meaning. We observed two interactions between imagery ability measured on the Florida Praxis Imagery Questionnaire (FPIQ) and BOI effects in semantic processing (response time and accuracy). In both interactions poorer imagery ability was associated with null BOI effects, whereas better imagery was associated with BOI effects. We also observed faster and more accurate responses to verbs associated with more foot/leg action meaning than verbs with less foot/leg action meaning, but this foot/leg action effect did not significantly interact with individual differences in motor imagery. In Experiment 2 (N = 195) we tested whether the interactions observed in Experiment 1 were dependent on the object-directed nature of the actions, or whether similar effects would be observed for hand actions not associated with objects. We also expanded our investigation beyond hand and foot imagery to consider whole body imagery. We observed an interaction between performance on a hand laterality judgement task (HLJT; assessing hand motor imagery) and sensorimotor effects in semantic processing of verbs associated with hand/arm action meaning. Participants with the fastest responses on the most difficult trials of the HLJT showed no significant difference in their response times to words with high and low hand/arm action meaning. We also observed faster and more accurate responses to high relative to low embodiment verbs, but this sensorimotor effect did not interact with individual differences in motor imagery. The results suggest specific (and not general) associations, in that some, but not all forms of hand and object-directed motor imagery are related to sensorimotor effects in language processing of hand/arm action verbs and nouns describing objects that are easy to interact with. As such, hand and object-directed motor imagery may share mechanisms with sensorimotor simulation during semantic processing.

“Not wanting to see it is hypocrisy, it's denying what is obvious”: Far‐right discriminatory discourses mobilised as common sense

AbstractThe far‐right recently entered the Portuguese parliament with the election of André Ventura, leader of the political party Chega. Since 2019, Chega has grown exponentially and has become the third political force. This study aimed to explore how Ventura represents different members of Portuguese society. We examine what meanings are reproduced to configure social representations about different category groups, adopting Critical Discourse Analysis tools to explore how they were mobilised as legitimate. We analysed 253 posts shared by Ventura on Facebook, Twitter, and Instagram from the 22nd of December 2020 to the 22nd of January 2021, a month before the 2021 presidential elections. Our analysis suggests that Ventura represents a reality in which only he can save the “good Portuguese” from the threats of three main enemies: Roma people, Black people, and so‐called “antifascist” activists. We discuss how those representations relate to what has been found in other contexts and their implications for the promotion of discrimination and marginalisation of these groups in Portugal. We also point out the potential benefits of integrating Critical Discourse Analysis methodological tools for the development of the Theory of Social Representations. Please refer to the Supplementary Material section to find this article's Community and Social Impact Statement.

Left regular bands of groups and the Mantaci–Reutenauer algebra

We develop the idempotent theory for algebras over a class of semigroups called left regular bands of groups (LRBGs), which simultaneously generalize group algebras of finite groups and left regular band (LRB) algebras. Our techniques weave together the representation theory of finite groups and LRBs, opening the door for a systematic study of LRBGs in an analogous way to LRBs. We apply our results to construct complete systems of primitive orthogonal idempotents in the Mantaci–Reutenauer algebra MRn[G] associated to any finite group G. When G is abelian, we give closed form expressions for these idempotents, and when G is the cyclic group of order two, we prove that they recover idempotents introduced by Vazirani.

Elementary construction of the minimal free resolution of the Specht ideal of shape (n − d,d)

Let K be a field with char(K)=0. For a partition λ of n∈N, let IλSp be the ideal of R=K[x1,…,xn] generated by all Specht polynomials of shape λ. These ideals have been studied from several points of view (and under several names). Using advanced tools of the representation theory, Berkesch Zamaere et al. [1] constructed a minimal free resolution of I(n−d,d)Sp except differential maps. The present paper constructs the differential maps, and also gives an elementary proof of the result of [1].

Tonal partition algebras: fundamental and geometrical aspects of representation theory

For we define tonal partition algebra over . We construct modules for over , and hence over any integral domain containing (such as ), that pass to a complete set of irreducible modules over the field of fractions. We show that is semisimple there. That is, we construct for the tonal partition algebras a modular system in the sense of Brauer. Using a “geometrical” index set for the Δ-modules, we give an order with respect to which the decomposition matrix over (with ) is upper-unitriangular. We establish several crucial properties of the Δ-modules. These include a tower property, with respect to n, in the sense of Green and Cox-Martin-Parker-Xi; contravariant forms with respect to a natural involutive antiautomorphism; a highest weight category property; and branching rules.

How does the Mass Media Represent the Concept of Electric Vehicles?

The number of electric vehicle sales has been increasing rapidly since 2015. This marketing success is inseparable from the role of the mass media in promoting and campaigning for the use of such vehicles. This study attempts to investigate how the mass media represents the concept of electric vehicles through its campaign and promotion discourses. Using a descriptive qualitative method with the interpretation technique, this study analyzed 20 texts collected from electric vehicle campaigns and promotion discourses produced by the mass media. The data was analyzed from the Critical Discourse Analysis perspective based on Hall's theory of representation and Fowler's theory of linguistic tools. This process resulted in 177 words, phrases, and clauses that represent the concept of electric vehicles. The results of this study reveal 4 (four) important representations of electric vehicles from the eye of the mass media; (1) electric vehicles are environmentally friendly, (2) electric vehicles are technologically advanced, (3) electric vehicles are economical, and (4) electric vehicles are a growing innovation. The results of this study are expected to bring both theoretical and practical contributions. Theoretically, they add to the knowledge in the realm of Critical Discourse Analysis, especially regarding representation. Meanwhile, practically, the results of this study are beneficial for mass media practitioners to be used as a model to construct campaign and advertisement languages that are able to attract audience attention as well as influence people's ideology.

Group Theory and Representation Theory

Group Theory and Representation Theory

Popularizing the Gay Characters: A Study of American Gay-Themed TV Series in 2000s

This study is a qualitative research which concentrates on the rise of TV series gay characters on American televisions starting in the early 2000s. The emergence of gay TV series in 2000s has made this phenomena interesting as well as essential to discuss since American television in the pre 2000s era was not not open about the gay characters in television series. The data for this study were obtained through a literature review consisting of journal articles as well as books. This study intended to identify why gay-themed TV series appeared in the 2000s by applying Hall’s theory of representation as a way for analyzing. This research is useful to an additional reference for other researchers and to increase people’s understanding on the gay TV series phenomenon in the US. The research findings showed that there at least four representations explaining the reasons for the emergence of gay-themed TV series in America – the progress of science and knowledge, the strength of minority, the state support, and the new target consumers.

On a family of Siegel Poincaré series

Let [Formula: see text] be a congruence subgroup of [Formula: see text]. Using Poincaré series of [Formula: see text]-finite matrix coefficients of integrable discrete series representations of [Formula: see text], we construct a spanning set for the space [Formula: see text] of Siegel cusp forms of weight [Formula: see text]. We prove the non-vanishing of certain elements of this spanning set using Muić’s integral non-vanishing criterion for Poincaré series on locally compact Hausdorff groups. Moreover, using the representation theory of [Formula: see text], we study the Petersson inner products of corresponding cuspidal automorphic forms, thereby recovering a representation-theoretic proof of some well-known results on the reproducing kernel function of [Formula: see text]. Our results are obtained by generalizing representation-theoretic methods developed by Muić in his work on holomorphic cusp forms on the upper half-plane to the setting of Siegel cusp forms of a higher degree.