Representation Theory Research Articles

ERST: A Signaled Graph Theory of Discourse Relations and Organization

Abstract In this article we present Enhanced Rhetorical Structure Theory (eRST), a new theoretical framework for computational discourse analysis, based on an expansion of Rhetorical Structure Theory (RST). The framework encompasses discourse relation graphs with tree-breaking, non-projective and concurrent relations, as well as implicit and explicit signals which give explainable rationales to our analyses. We survey shortcomings of RST and other existing frameworks, such as Segmented Discourse Representation Theory (SDRT), the Penn Discourse Treebank (PDTB) and Discourse Dependencies, and address these using constructs in the proposed theory. We provide annotation, search and visualization tools for data, and present and evaluate a freely available corpus of English annotated according to our framework, encompassing 12 spoken and written genres with over 200K tokens. Finally, we discuss automatic parsing, evaluation metrics and applications for data in our framework.

On Bethe equations of 2d conformal field theory

We study the higher spin algebras of two-dimensional conformal field theory from the perspective of quantum integrability. Starting from Maulik-Okounkov instanton R-matrix and applying the procedure of algebraic Bethe ansatz, we obtain infinite commuting families of Hamiltonians of quantum ILW hierarchy parametrized by the shape of the auxiliary torus. We calculate explicitly the first five of these Hamiltonians. Then, we numerically verify that their joint spectrum can be parametriezed by solutions of Litvinov’s Bethe ansatz equations and we conjecture a general formula for the joint spectrum of all ILW Hamiltonians, based on results of Feigin, Jimbo, Miwa and Mukhin.There are two interesting degeneration limits, the infinitely thick and the infinitely thin auxiliary torus. In one of these limits, the ILW hierarchy degenerates to Yangian or Benjamin-Ono hiearchy and the Bethe equations can be easily solved. The other limit is singular but we can nevertheless extract local Hamiltonians corresponding to quantum KdV or KP hierarchy. Litvinov’s Bethe equations in this local limit provide an alternative to Bethe ansatz equations of Bazhanov, Lukyanov and Zamolodchikov, but are more transparent, work at any rank and are manifestly symmetric under triality symmetry of W\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{W} $$\\end{document}1+∞. Finally, we illustrate analytic properties of the solutions of Bethe equations in minimal models, in particular for Lee-Yang CFT. The analytic structure of Bethe roots is very rich as it captures the representation theory of W\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{W} $$\\end{document}N minimal models.

Decompositions of Hyperbolic Kac–Moody Algebras with Respect to Imaginary Root Groups

We propose a novel way to define imaginary root subgroups associated with (timelike) imaginary roots of hyperbolic Kac–Moody algebras. Using in an essential way the theory of unitary irreducible representation of covers of the group SO(2, 1), these imaginary root subgroups act on the complex Kac–Moody algebra viewed as a Hilbert space. We illustrate our new view on Kac–Moody groups by considering the example of a rank-two hyperbolic algebra that is related to the Fibonacci numbers. We also point out some open issues and new avenues for further research, and briefly discuss the potential relevance of the present results for physics and current attempts at unification.

Creating communities that care: social representation of mental health in two urban poor communities in Ghana

Building caring communities is fundamental to achieving a community-based approach to mental health. Understanding how communities perceive mental illness provides critical insight into fostering mental health awareness and care. We explored the perceptions of mental illness among members of two urban poor communities in Accra, Ghana. Qualitative data were collected from 77 participants through key informant interviews, focus group discussions, and situated conversations. Using theory-driven thematic analysis based on social representations theory, findings revealed cognitive-emotional representations of mental illness. The communities demonstrated high awareness of the multilevel factors contributing to mental illness risk and experiences, drawing on five sources of knowledge: embodied, common sense, medical, cultural, and religious. Mental illness representations informed the classification and legitimization of mental illness based on the severity of conditions and the identity of sufferers. These findings provide valuable insights for planning community mental health interventions that address both social and institutional care needs.

Unveiling Violence and Masculinity through a Psychoanalytic Study of Sam Shepard's Curse of the Starving Class (1977), Sarah Kane' Blasted (1995) and The Body of a Woman as a Battlefield in Bosnian War (1996) by Matei Visniec

The examination of violence and its association with masculinity is depicted in three distinct plays: Blasted, written by Sarah Kane in 1995; Curse of the Starving Class, authored by Sam Shepard in 1977 (it was made into a Hollywood film in 1994); and Matei Vişniec’ The Body of a Woman as a Battlefield in the Bosnian War (1996). Utilizing a qualitative approach, this study employs close textual analysis and an extensive review of relevant literature to examine the representation of violence and masculinity in theatrical framework while also exploring the wider societal implications of such portrayals. The chosen plays present a wide range of viewpoints regarding violence, encompassing both highly intense manifestations of violence and the repercussions of warfare on the individuals. This analysis utilizes Judith Butler's theory of gender construction and Antonio Artaud's Theatre of Cruelty in order to examine the ways in which these plays either challenge or uphold conventional gender. Furthermore, it investigates the intricate correlation between trauma and aggressive conduct as depicted in the plays. By going deeply into the text and exploring its underlying concepts, it reveals the crucial function of theater in tackling and evaluating complex social problems. The plays act as a mirror for society viewpoints, forcing readers and the audiences to face uncomfortable truths about aggression, masculinity, and emotional anguish. The impacts of trauma on individuals and communities are brought to light. These plays demonstrate how war trauma can induce rage and promote violent behavior. It also highlights the power of theater to challenge harmful social conventions and catalyze positive social change by challenging traditional gender roles and power dynamics. Improving the audiences understanding of cultural attitudes and potential paths for societal change, this study contributes significantly to the assessment of violence and masculinity as depicted in theatrical performances.

Power, interests and representations in the construction of alcopop as public problem in Quebec, Canada

Alcopops are malt-based or spirit-based sugary beverages whose consumption has led to numerous policies in different Western countries. This article examines the representational and socio-political dynamics surrounding the sale of alcopops that led to restrictive policies in Canada (2017–2020). Using qualitative methods during this period, including interviews with key players in the field of alcohol policy, analysis of press articles and review of legislative documents, we trace the evolution of public and political discourse on alcopops. We shed light on the role of social actors—mainly public-health organizations and the alcohol industry—defending their own interests to influence policy-making. A multi-theoretical framework is used to analyze how alcopops emerged as a public problem. This framework integrates Herbert Blumer's theoretical perspective on social problems, Serge Moscovici's social representation theory and Stevens and Zampini’s political constellation model. Through an analysis of the socio-political context in Quebec, we reveal the complex interplay between public health imperatives and the interests of the alcohol industry. This should serve as a model to study public problems that lead to public policies implementation.

A Mathematical World Woven by Number Theory, Algebraic Geometry, and Representation Theory

A Mathematical World Woven by Number Theory, Algebraic Geometry, and Representation Theory

Representation Theory and Combinatorics Arising from Determinants

Representation Theory and Combinatorics Arising from Determinants

Xiaomei Chen. Performing the Socialist State: Modern Chinese Theater and Film Culture

This book presents a nuanced, revisionist exploration of the development of modern and contemporary Chinese theatre and related arts, challenging the conventional demarcations between Republican, high socialist, and post-socialist periods. It discloses subtle entanglements in theatre theory and practice, underscoring the persistent approaches to aesthetics and politics across eras and theatrical genres.

Symmetry and Representation Theory of Lie Groups and Lie Algebras

Symmetry and Representation Theory of Lie Groups and Lie Algebras

On modulo ℓ cohomology of p-adic Deligne–Lusztig varieties for GLn

In 1976, Deligne and Lusztig realized the representation theory of finite groups of Lie type inside étale cohomology of certain algebraic varieties. Recently, a p-adic version of this theory started to emerge: there are p-adic Deligne–Lusztig spaces, whose cohomology encodes representation theoretic information for p-adic groups – for instance, it partially realizes the local Langlands correspondence with characteristic zero coefficients. However, the parallel case of coefficients of positive characteristic ℓ≠p has not been inspected so far. The purpose of this article is to initiate such an inspection. In particular, we relate cohomology of certain p-adic Deligne–Lusztig spaces to Vignéras's modular local Langlands correspondence for GLn.

ACCOMPAGNEMENT DES ENFANTS AUTISTES A LEPREUVE DES REPRESENTATIONS SOCIALES DES ORTHOPHONISTES : UNE APPROCHE PSYCHOSOCIALE

This article sets two main objectives. The first consists of identifying the social representations of autism among Moroccan speech therapists. The second objective consists of analyzing the impact of these social representations on the communication support practices of children with autism spectrum disorder (ASD). Although several studies have addressed the problem of autism, especially with the increase in the number of children suffering from this disorder in recent decades, few have approached it from the angle of the theory of social representations in context Moroccan. In this article, we used the psychosocial approach, with the theory of social representations of Moscovici (1961) to understand how speech therapists who are supposed to welcome and support autistic children construct their social representations on the autism. The empirical investigation is part of a mixed study, combining an exploratory qualitative method and a quantitative method. Indeed, our study took place in two parts: The first qualitative one was carried out through a free association questionnaire (the inducing word is autism) with 80 Moroccan speech therapists working in the private and public sector. Then, we used the hierarchical evocation technique of P. Vergès (1992) to show the importance of expressions and to assess their knowledge about autism. The second step, quantitative, makesit possible to collect quantitative data with the aim of illustrating the qualitative data obtained previously, and to understand the reality as objectively as possible, of the impact of social representations of autism among speech therapists on communication support practices for autistic children. Finally, we proceed to a discussion of the results obtained through this research.

From free fields to interacting SCFTs via representation theory

We ask when it is possible to construct arbitrary unitary multiplets of the superconformal algebra with eight Poincaré supercharges that are compatible with locality from (continuous deformations of) representations in free field theories. We answer this question in two, three, and five dimensions. In four dimensions, we resort to an intricate but self-consistent web of conjectures. If correct, these conjectures imply various new non-perturbative constraints on short multiplets in any local unitary 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 superconformal field theory and on an unusual set of related vertex algebras. Throughout, we connect our results with properties of deformations in the space of theories.

A representation theory for modal distributive lattices

A representation theory for modal distributive lattices

Information-based Gradient enhanced Causal Learning Graph Neural Network for fault diagnosis of complex industrial processes

By representing the embedded components and their interactions in industrial systems as nodes and edges in a graph, Graph Neural Networks (GNNs) have achieved outstanding results due to their ability to model statistical correlations. However, these correlations may not capture the true causal relationships within the data, thereby impairing the model’s performance in fault diagnosis.To address this issue, an Information-based Gradient enhanced Causal Learning Graph Neural Network (IGCL-GNN) is proposed for fault diagnosis of complex industrial processes. First, the information theory in graph representations is theoretically analyzed and the optimization objectives are derived separately for the causal and non-causal parts of the graph neural network, which decouple it into a multi-objective optimization problem. Then, to optimize such problem, a causal disentanglement layer is designed in the graph network that could effectively separate causal and non-causal information in graph representations. Thirdly, a novel gradient reactivation method is proposed to dynamically filter features from the disentangled layers, thereby capture the causal representations of graph data more accurately. For robust and efficient optimization, the multi-objective gradient descent algorithm is employed in this paper. Finally, comparative experiments were conducted on the three-phase flow facility (TFF) dataset, achieving a fault diagnosis accuracy of 98.42% for our proposed method.

Enumeration and Representation Theory of Spin Space Groups

Fundamental physical properties, such as phase transitions, electronic structures, and spin excitations, in all magnetic ordered materials, were ultimately believed to rely on the symmetry theory of magnetic space groups. Recently, it has come to light that a more comprehensive group, known as the spin space group (SSG), which combines separate spin and spatial operations, is necessary to fully characterize the geometry and underlying properties of magnetic ordered materials. However, the basic theory of SSG has seldom been developed. In this work, we present a systematic study of the enumeration and the representation theory of the SSG. Starting from the 230 crystallographic space groups and finite translation groups with a maximum order of eight, we establish an extensive collection of over 100 000 SSGs under a four-index nomenclature as well as international notation. We then identify inequivalent SSGs specifically applicable to collinear, coplanar, and noncoplanar magnetic configurations. To facilitate the identification of the SSG, we develop an online program that can determine the SSG symmetries of any magnetic ordered crystal. Moreover, we derive the irreducible corepresentations of the little group in momentum space within the SSG framework. Finally, we illustrate the SSG symmetries and physical effects beyond the framework of magnetic space groups through several representative material examples, including a candidate altermagnet RuO2, spiral spin polarization in the coplanar antiferromagnet CeAuAl3, and geometric Hall effect in the noncoplanar antiferromagnet CoNb3S6. Our work advances the field of group theory in describing magnetic ordered materials, opening up avenues for deeper comprehension and further exploration of emergent phenomena in magnetic materials. Published by the American Physical Society 2024

Enumeration of Spin-Space Groups: Toward a Complete Description of Symmetries of Magnetic Orders

Symmetries of three-dimensional periodic scalar fields are described by 230 space groups (SGs). Symmetries of three-dimensional periodic (pseudo)vector fields, however, are described by the spin-space groups (SSGs), which were initially used to describe the symmetries of magnetic orders. In SSGs, the real-space and spin degrees of freedom are unlocked in the sense that an operation could have different spatial and spin rotations. SSGs give a complete symmetry description of magnetic structures and have natural applications in the band theory of itinerary electrons in magnetically ordered systems with weak spin-orbit coupling. , a concept raised recently that belongs to the symmetry-compensated collinear magnetic orders but has nonrelativistic spin plitting, is well described by SSGs. Because of the vast number and complicated group structures, SSGs have not yet been systematically enumerated. In this work, we exhaust SSGs based on the invariant subgroups of SGs, with spin operations constructed from three-dimensional (3D) real representations of the quotient groups for the invariant subgroups. For collinear and coplanar magnetic orders, the spin operations can be reduced into lower-dimensional real representations. As the number of SSGs is infinite, we consider only SSGs that describe magnetic unit cells up to 12 times crystal unit cells. We obtain 157 289 noncoplanar, 24 788 coplanar-noncollinear, and 1421 collinear SSGs. The enumerated SSGs are stored in an online database with a user-friendly interface. We develop an algorithm to identify SSGs for realistic materials and find SSGs for 1626 magnetic materials. We also discuss several potential applications of SSGs, including the representation theory, topological states protected by SSGs, structures of spin textures, and refinement of magnetic neutron diffraction patterns using SSGs. Our results serve as a solid starting point for further studies of symmetry and topology in magnetically ordered materials. Published by the American Physical Society 2024

Property as power: A theory of representation

Property as power: A theory of representation

A generalized dynamic asymmetric exclusion process: orthogonal dualities and degenerations

Abstract In this paper, a generalized version of dynamic asymmetric simple exclusion process (ASEP) is introduced, and it is shown that the process has a Markov duality property with the same process on the reversed lattice. The duality functions are multivariate q-Racah polynomials, and the corresponding orthogonality measure is the reversible measure of the process. By taking limits in the generator of dynamic ASEP, its reversible measure, and the duality functions, we obtain orthogonal and triangular dualities for several other interacting particle systems. In this sense, the duality of dynamic ASEP sits on top of a hierarchy of many dualities. For the construction of the process, we rely on representation theory of the quantum algebra U q ( sl 2 ) . In the standard representation, the generator of generalized ASEP can be constructed from the coproduct of the Casimir. After a suitable change of representation, we obtain the generator of dynamic ASEP. The corresponding intertwiner is constructed from q-Krawtchouk polynomials, which arise as eigenfunctions of twisted primitive elements. This gives a duality between dynamic ASEP and generalized ASEP with q-Krawtchouk polynomials as duality functions. Using this duality, we show the (almost) self-duality of dynamic ASEP.

Embodied spatial metaphor of cultural concept from the perspective of cultural tightness–looseness: Cultural compatibility concept is closer to the body

AbstractThe body carries culture, with cultural concepts emerging from the dynamic interplay between the body and its environment. By integrating social representation theory and embodied cognition, we explored the use of embodied spatial metaphors in representing cultural tightness–looseness across three studies. In Study 1, 84 participants were randomly assigned to either a tight or loose culture group and tasked with placing cultural words within a spatial context. Participants positioned culturally compatible words closer to themselves and incompatible words farther away, illustrating the use of spatial distance metaphors to represent cultural tightness–looseness. Study 2 used an implicit task, demonstrating that people from both tight and loose cultures exhibited greater accuracy in judging culturally compatible concepts (vs. incompatible concepts) when these words were close to themselves. Study 3 unveiled distinct patterns of embodied spatial metaphors between tight and loose cultures when comparing cultural and irrelevant words. Notably, metaphors depicting nearness for culturally compatible words and farness for irrelevant words emerged exclusively in tight cultures, while such patterns were absent in loose cultures. Overall, our findings empirically support the notion that social representations are embodied, and provide embodied evidence for understanding and representing concepts related to cultural tightness–looseness.