On the distribution of the periods of convex representations II
Abdelhamid Amroun
Let $ρ: Γ\longrightarrow G$ be a Zariski dense irreducible convex representation of the hyperbolic group $Γ$, where G is a connected real semisimple algebraic Lie group. We establish a central limit type theorem for the periods of the representation $ρ$.
On Speh representations for level zero supercuspidal representations and Ginzburg-Kaplan gamma factors
Elad Zelingher
We establish a relation between Speh representations of $\mathrm{GL}_n\left(\mathbb{F}_q\right)$ and Speh representations of $\mathrm{GL}_n\left(F\right)$, where $F$ is a non-archimedean local field. We use irreducible level zero supercuspidal representations to show that these two notions of Speh representations associated to cuspidal representations are related via a commutative diagram, and that their corresponding $(k,c)$ $ψ$-Whittaker models are also related. We use these results to relate the local Ginzburg-Kaplan integrals for level zero supercuspidal representations to their finite field counterparts.
Resolutions for Locally Analytic Representations
Shishir Agrawal, Matthias Strauch
The purpose of this paper is to study resolutions of locally analytic representations of a $p$-adic reductive group $G$. Given a locally analytic representation $V$ of $G$, we modify the Schneider-Stuhler complex (originally defined for smooth representations) so as to give an `analytic' variant ${\mathcal S}^A_\bullet(V)$. The representations in this complex are built out of spaces of analytic vectors $A_σ(V)$ for compact open subgroups $U_σ$, indexed by facets $σ$ of the Bruhat-Tits building of $G$. These analytic representations (of compact open subgroups of $G$) are then resolved using the Chevalley-Eilenberg complex from the theory of Lie algebras. This gives rise to a resolution ${\mathcal S}^{\rm CE}_{q,\bullet}(V) \rightarrow {\mathcal S}^A_q(V)$ for each representation ${\mathcal S}^A_q(V)$ in the analytic Schneider-Stuhler complex. In a last step we show that the family of representations ${\mathcal S}^{\rm CE}_{q,j}(V)$ can be given the structure of a Wall complex. The associated total complex ${\mathcal S}^{\rm CE}_\bullet(V)$ has then the same homology as that of ${\mathcal S}^A_\bullet(V)$. If the latter is a resolution of $V$, then one can use ${\mathcal S}^{\rm CE}_\bullet(V)$ to find a complex which computes the extension group $\underline{Ext}^n_G(V,W)$, provided $V$ and $W$ satisfy certain conditions which are satisfied when both are admissible locally analytic representations.
The Cayley Transform on Representations
Jingyu Lu, Ke Ye
The classical Cayley transform is a birational map between a quadratic matrix group and its Lie algebra, which was first discovered by Cayley in 1846. Because of its essential role in both pure and applied mathematics, the classical Cayley transform has been generalized from various perspectives. This paper is concerned with a representation theoretic generalization of the classical Cayley transform. The idea underlying this work is that the applicability of the classical Cayley transform heavily depends on how the Lie group is represented. The goal is to characterize irreducible representations of a Lie group, to which the classical Cayley transform is applicable. To this end, we first establish criteria of the applicability for a general Lie group. If the group is semisimple, we further obtain a geometric condition on the weight diagram of such representations. Lastly, we provide a complete classification for classical complex simple Lie groups and their compact real forms. Except for the previously known examples, spin representations of $\mathrm{Spin}(8)$ are the only ones on our list.
Representations of $SL_2(F)$
Guy Henniart, Marie-France Vignéras
Let $p$ be a prime number, $F $ a non-archimedean local field with residue characteristic $p$, and $R$ an algebraically closed field of characteristic different from $ p$. We thoroughly investigate the irreducible smooth $R$-representations of $SL_2(F)$. The components of an irreducible smooth $R$-representation $Π$ of $GL_2(F)$ restricted to $SL_2(F)$ form an $L$-packet $L(Π)$. We use the classification of such $Π$ to determine the cardinality of $L(Π)$, which is $1,2$ or $4$. When $p=2$ we have to use the Langlands correspondence for $GL_2(F)$. When $\ell$ is a prime number distinct from $p$ and $R=\mathbb Q_\ell^{ac}$, we establish the behaviour of an integral $L$-packet under reduction modulo $\ell$. We prove a Langlands correspondence for $SL_2(F)$, and even an enhanced one when the characteristic of $R$ is not $2$. Finally, pursuing a theme of \cite{HV23}, which studied the case of inner forms of $GL_n(F)$, we show that near identity an irreducible smooth R-representation of $SL_2(F)$ is, up to a finite dimensional representation, isomorphic to a sum of $1,2$ or $4$ representations in an $L$-packet of size $4$ (when $p$ is odd there is only one such $L$-packet).
Poésies de la naissance dans les spectacles de Joël Pommerat
Cécile Auzolle
Depuis les années 1990, les spectacles de Joël Pommerat explorent la dimension sensible du monde contemporain. L’enfant y cristallise l’amour, la haine ou la projection des familles. Les marchands (2006), Au monde (2004), La réunification des deux Corées (2013) et Des suées (1993) révèlent les arcanes de la conception. Cet enfant (2006) montre comment la gestation modèle le parent en devenir. Deux scènes de mise au monde, issues de Cet enfant et de Pinocchio (2008), permettent enfin de mettre en lumière les attentes et les angoisses entourant la découverte d’un être semblable et étranger à son·sa géniteur·trice, en miroir du processus de création artistique.
Dramatic representation. The theater
A interculturalidade nos trabalhos do Teatro da Travessia: a cultura como performance
Francisco Wagner Bezerra Rodrigues
O objetivo principal deste ensaio é fazer uma análise das experiências de criação do grupo teatral brasileiro Teatro da Travessia com o diretor Philippe Goudard (França) e com o grupo teatral Cie. Singulier Pluriel (Québec), tendo como material norteador da reflexão conceitos como cultura, fronteiras, grupos étnicos, entre outros. Utilizamos como material suplementar o conceito de cultura tal como é vista no campo da performance, tendo como referência os escritos de Richard Schechner e Diana Taylor. A ideia de colocar esses conceitos lado a lado é de propor uma análise dos mesmos mais diretamente ligada ao campo teatral. Mais que tentar definir o que é cada um dos conceitos, propomos aqui uma reflexão, por assim dizer, performativa, pois que será também um saber enquanto se faz, um entender em processo.
The performing arts. Show business, Drama
From the Editors
Pamiętnik Teatralny
Short editorial introduction to Pamiętnik Teatralny 71, no. 4 (2022).
Dramatic representation. The theater, The performing arts. Show business
Representations of Munn algebras and related semigroups
Yuriy A. Drozd, Andriana I. Plakosh
We establish representation types (finite, tame or wild) of finite dimensional Munn algebras with semisimple bases. As an application, we establish representation types of finite 0-simple semigroups and their mutually annihilating unions.
Em Busca da Sabrosura e do Sabor: encontros possíveis entre método antropológico e performance
Pilar Cabanzo
O artigo propõe articulações entre método antropológico e performance a partir de dados coletados em uma investigação sobre a dança de salsa na cidade do Rio de Janeiro. O texto narra mudanças na abordagem da salsa, centrando-se em dois modos específicos e distintos praticados em duas academias de dança de salão. A literatura sobre salsa costuma privilegiar sua estrutura sonora, deixando de lado outros estímulos sensoriais. Em contraste, no presente texto se realiza uma abordagem etnográfica da dança de salsa atrelada a noções de performance. Assim, procura-se trazer contribuições para a pesquisa em dança a partir de uma perspectiva antropológica.
Drama, Dramatic representation. The theater
First-person Narrative in the Performative Practice of Marginalized Women and Decolonial Knowledge Production
Caroline Dias de Oliveira Silva
First-Person Narrative in the Performative Practice of Marginalized Women and Decolonial Knowledge Production – The essay proposes a dialogue between feminist decolonial thinking and performance art, as they connect to my own experience in these fields. Based on the understanding that the decolonial perspective puts all Western conceptual and methodological categorizations under critical scrutiny, my objective is to advance discussion of performance by marginalized women, seeking to understand their role in the production of shared meanings through disruptive and anti-colonial writing. To this end, I examine performative actions that deploy such practices, which I understand as initiatives toward decolonization through embodied expression
Drama, Dramatic representation. The theater
« Devenir-soma » : la création littéraire par des ateliers somatiques d’écriture
Mattia Scarpulla
Depuis 2015, j’organise des ateliers somatiques d’écriture à l’occasion de processus de spectacles littéraires, mais aussi dans le cadre de formations données à l’université ou dans des centres consacrés à la littérature. Durant ces ateliers, les auteur·trices sont plongé·es dans une mise en chorégraphie, exécutent des exercices de respiration et de yoga, des automassages Do-In, chacun·e produisant une création littéraire en lien avec son ressenti. Dans mon article, j’introduis deux expériences immersives, l’une qui a eu lieu à Turin en 2018, et l’autre que j’ai animée à Québec en 2019. Les participant·es y ont déployé une poétique somatique, en créant une oeuvre littéraire et un solo de danse les yeux fermés.
Dramatic representation. The theater
Representation stability and outer automorphism groups
Luca Pol, Neil P. Strickland
In this paper we study families of representations of the outer automorphism groups indexed on a collection of finite groups $\mathcal{U}$. We encode this large amount of data into a convenient abelian category $\mathcal{A}\mathcal{U}$ which generalizes the category of VI-modules appearing in the representation theory of the finite general linear groups. Inspired by work of Church--Ellenberg--Farb, we investigate for which choices of $\mathcal{U}$ the abelian category is locally noetherian and deduce analogues of central stability and representation stability results in this setting. Finally, we show that some invariants coming from rational global homotopy theory exhibit representation stability.
From Movement to Sound, from Sound to Movement: biocultural relations between dance and music
Andréia Nhur
This article discusses the interactions between body and sound in the creative process characterized by the relation between dance, music and sonic experiments. Based on the production Peças Fáceis, by Pró-Posição Group, and Z, by Alejandro Ahmed, this study presents theoretical approaches between Dance Studies and Embodied Music Cognition fields. It also intends to discuss what happens to the bodily perception and mediation process in artists who dance, play musical instruments and produce vocal sounds. The analyzed plays, each one in its way, defend the idea that sound and movement are no-concluded processes crossed constantly by mutual and biocultural interactions with the environment.
Drama, Dramatic representation. The theater
Écritures théâtrales françaises et dramaturgies d’Afrique et des diasporas : une aventure ambiguë?
Pénélope Dechaufour
Cet article revient sur les réseaux d’émergence des écritures d’Afrique subsaharienne francophone et d’Outre-Mer. Il pose la question de leur place dans le paysage des écritures françaises d’aujourd'hui. En effet, cette place ne va pas de soi alors qu’en remontant le fil de l’histoire on comprend que ces écritures soient assez logiquement prises dans le maillage des dramaturgies de la France hexagonale. Après un aperçu historique des différentes générations d’auteur·trices et des circuits qui leur ont permis d’émerger depuis les années 1970, l’article interroge l’évolution de ce rapport aux institutions du spectacle vivant ces dernières décennies. En proposant un état des lieux des principaux·pales auteur·trices actuellement remarqué·es, nous dressons une cartographie à la fois éditoriale et institutionnelle qui montre l’interdépendance des réseaux d’auteur·trices avec les politiques culturelles françaises qui n’ont de cesse pourtant de les renvoyer dans des espaces dédiés. Les auteur·trices contemporain·es d’Afrique et des diasporas sont pris·es dans une situation inextricable qui est le fruit de l’histoire coloniale. Devenu·es ces dernières années de véritables acteur·trices culturel·les dans leur pays d’origine, c’est par ce biais que des partenariats institutionnels se nouent avec les pays dits du « Nord » et que ces auteur·trices-directeur·trices de festivals assurent leur propre visibilité dans le paysage des dramaturgies françaises et francophones qui leur offre publication et statut professionnel. Mais pourquoi sont-il·elles tout de même si peu visibles ou renvoyé·es dans des espaces de la marge? Quels sont les impacts de ces phénomènes sur le plan esthétique? Qu’est-ce qui explique une telle situation et que faut-il encore déconstruire dans le regard occidental pour que ces écritures soient réellement comprises et affranchies d’un certain nombre de tâches qui étouffent encore et toujours la création? L’article tente d’apporter des réponses à cette fusion-disjonction entre écritures « d’Afrique et des diasporas » et « écritures françaises ».
Dramatic representation. The theater
Inter Faces: creation processes for artistic performance enhanced by augmented reality
Régis Costa de Oliveira, Mónica Sofia Santos Mendes, Anselmo Cardoso de Paiva
Inter Faces: creation processes for artistic performance enhanced by augmented reality – In view of the poetic use of augmented reality, this article presents links between performance and augmented reality technology with self-referenced digital content, supported by the activist artistic proposal Inter Faces. For a reflection on creative processes, the artistic works body and Parade to Hope are compared. With this analysis we intend to present the challenges and solutions found during the creation process of Inter Faces, seeking to contribute to the debate on the expansion, popularization and poetization of augmented reality in performance.
Drama, Dramatic representation. The theater
Bugged (Critics, Criticism and Critical Categories)
Don Rubin
Dramatic representation. The theater
Affine Hecke algebras and their representations
Maarten Solleveld
This is a survey paper about affine Hecke algebras. We start from scratch and discuss some algebraic aspects of their representation theory, referring to the literature for proofs. We aim in particular at the classification of irreducible representations. Only at the end we establish a new result: a natural bijection between the set of irreducible representations of an affine Hecke algebra with real parameters $\geq 1$, and the set of irreducible representations of the affine Weyl group underlying the algebra. This can be regarded as a generalized Springer correspondence with affine Hecke algebras.
Percées exploratoires
Jean-Paul Quéinnec, Catherine Cyr
Dramatic representation. The theater
On calibrated representations of the degenerate affine periplectic Brauer algebra
Zajj Daugherty, Iva Halacheva, Mee Seong Im
et al.
We initiate the representation theory of the degenerate affine periplectic Brauer algebra on $n$ strands by constructing its finite-dimensional calibrated representations when $n=2$. We show that any such representation that is indecomposable and does not factor through a representation of the degenerate affine Hecke algebra occurs as an extension of two semisimple representations with one-dimensional composition factors; and furthermore, we classify such representations with regular eigenvalues up to isomorphism.