Supercuspidal representations: construction, classification, and characters
Jessica Fintzen
The building blocks for irreducible smooth representations of p-adic groups are the supercuspidal representations. In these notes that are an expansion of a lecture series given during the IHES summer school 2022 we will explore an explicit exhaustive construction of these supercuspidal representations and their character formulas and observe a striking parallel between a large class of these representations and discrete series representations of real algebraic Lie groups. A key ingredient for the construction of supercuspidal representations is the Bruhat-Tits theory and Moy-Prasad filtration, which we will recall in this survey.
ТИШИНА В ПРОСТРАНСТВЕ СОВРЕМЕННОЙ ХОРЕОГРАФИИ
Вейзанс E., Канат Ж.
Объектом изучения в предложенной статье является
современная хореография, активно переосмысливающая
взаимодействие музыки и движения, включая концепцию
тишины как художественного элемента. Методы исследования
включают культурно-исторический и сравнительный анализ.
Актуальность и новаторство статьи заключаются в анализе
постановок, в которых тишина становится самостоятельным
выразительным средством. В исследовании
проанализированы постановки, в которых тишина является
художественным образом, создает новые формы выражения,
влияет на технику (хореографические постановки Карлоса
Карвахаля, Начо Дуато, Иржи Килиана, Уильяма Форсайта,
Мартина Шекса и др.). В постмодернистских постановках
тишина выступает в роли символа, структурного элемента
танца, средства драматургического воздействия.
Акцентируется внимание на воздействие восточных традиций
и перформативных практик, рассматриваются образцы
синтеза восточных и западных традиций в хореографии,
обосновывающих концепцию статьи: тишина в танце — это не
просто отсутствие звука, а мощный инструмент
художественного выражения.
The performing arts. Show business, Dramatic representation. The theater
Rafał Węgrzyniak (1960–2024)
Wspomnienie o Rafale Węgrzyniaku (1960–2024), historyku teatru, krytyku teatralnym i redaktorze Pamiętnika Teatralnego w latach 1991–1997. Węgrzyniak swoim myśleniem o teatrze i rozpiętością zainteresowań bliski był ideom Zbigniewa Raszewskiego. We wspomnieniu przypomniano przebieg pracy Węgrzyniaka, napisane przez niego książki i teksty. Wspomnienie uzupełnia bibliografia tekstów Rafała Węgrzyniaka opublikowanych w Pamiętniku Teatralnym.
Dramatic representation. The theater, The performing arts. Show business
Courage, Capacity, Earth-Diving: Riting Safe(r) Spaces Down in the “Muck”
Julie Burelle, Jill Carter
Dramatic representation. The theater
Spór o mangę – rzut oka z perspektywy badacza komiksu
Wojciech Birek
The article is an attempt to analyse the methods and critical arguments against the manga and anime expressed by the people who, in the polemical discourse of their opponents, are treated as experts. The analysis focuses mostly on articles by Małgorzata Więczkowska, highlighting the constant crypto-self-quotations and the repeating of factual errors and steoreotypical biases. In these texts, one can notice i.e. the generalisation of accusations based on opinions on particular titles, describing the entire phenomenon through the characteristics of selected types and genres, the lack of any distinction being made between manga and anime, and lastly, a superficial understanding of the works in question, whose content and message the author often extrapolates from an overview, without taking the specifics of each work into account.
Photography, Dramatic representation. The theater
Unitary $L^{p+}$-representations of almost automorphism groups
Antje Dabeler, Emilie Mai Elkiær, Maria Gerasimova
et al.
Let $G$ be a locally compact group with an open subgroup $H$ with the Kunze-Stein property, and let $π$ be a unitary representation of $H$. We show that the representation $\widetildeπ$ of $G$ induced from $π$ is an $L^{p+}$-representation if and only if $π$ is an $L^{p+}$-representation. We deduce the following consequence for a large natural class of almost automorphism groups $G$ of trees: For every $p \in (2,\infty)$, the group $G$ has a unitary $L^{p+}$-representation that is not an $L^{q+}$-representation for any $q < p$. This in particular applies to the Neretin groups.
Dançando o phásma: a performance do conflito sírio na dança-teatro contemporânea
Sílvia Raposo
Este artigo propõe uma análise da dança teatral a partir do binômio performance/política, no qual o corpo é visto como um lugar privilegiado para a análise do poder, uma vez que um corpo que dança sempre toma uma posição no campo político. Para fazer isso, tentamos contextualizar a dança-teatro das peças "Antes que Matem os Elefantes", da Companhia Olga Roriz, e "Eu Sou Mediterrâneo", da Companhia Vidas de A a Z, em seu percurso artístico e analisar suas linguagens coreográficas e cênicas, tendo em vista uma compreensão do corpo que dança como um corpo que sofre as ações das relações de poder, analisando-o como um lugar de tensão e confrontos que desenvolve articulações com a memória e o esquecimento em um jogo sensorial-corporal, falando do corpo como um arquivo e como um lugar de memória e resistência, e olhando para ele como um lugar privilegiado para a análise do poder.
Dramatic representation. The theater
Archiviare l’effimero: la permanenza della danza di Dunhuang attraverso le tecnologie
Xiao Huang
L’articolo, solidamente fondato su fonti e documenti inediti nel panorama occidentale, ricostruisce un episodio di raro interesse per la storia delle arti performative cinesi e mondiali, basato su un processo di traduzione tra medium e linguaggi diversi che portò alla realizzazione dello spettacolo di danza teatrale Pioggia di fiori sulla Via della Seta (1979), partendo dallo studio degli affreschi delle grotte di Dunhuang (IV-XIV secolo d.C) - contesto in cui emersero anche i primi pionieristici esperimenti di notazione scritta della danza - per poi tradurlo successivamente in dance film nel 1982, in TV show nel 2008 e in video digitale virale nel 2021: un passaggio dalla bidimensionalità delle posizioni statiche della pittura, alla quadridimensionalità dei corpi in movimento dei danzatori, fino ad arrivare all’applicazione del linguaggio cinematografico per trascrivere le coreografie su schermo, e alle potenzialità di diffusione digitale dei social, e della motion capture.
Le raffigurazioni di creature mitologiche, di danzatori e musici, dipinte dal IV al XIV secolo d.C. sulle pareti delle grotte di Mogao quasi si trattasse di un archivio di pose coreutiche, furono utilizzate per ricostruire le coreografie di danze tradizionali antiche. Il concetto di archivio potrebbe essere altresì applicato alla fase della traduzione filmica, che ha consentito la permanenza e la trasmissione di quella coreografia, e del suo odierno corrispettivo digitale e social.
Dramatic representation. The theater
Polynomial representations of the Witt Lie algebra
Steven V Sam, Andrew Snowden, Philip Tosteson
The Witt algebra W_n is the Lie algebra of all derivations of the n-variable polynomial ring V_n=C[x_1, ..., x_n] (or of algebraic vector fields on A^n). A representation of W_n is polynomial if it arises as a subquotient of a sum of tensor powers of V_n. Our main theorems assert that finitely generated polynomial representations of W_n are noetherian and have rational Hilbert series. A key intermediate result states polynomial representations of the infinite Witt algebra are equivalent to representations of Fin^op, where Fin is the category of finite sets. We also show that polynomial representations of W_n are equivalent to polynomial representations of the endomorphism monoid of A^n. These equivalences are a special case of an operadic version of Schur--Weyl duality, which we establish.
Extensions of theorems of Gaschütz, Žmud$'$ and Rhodes on faithful representations
Benjamin Steinberg
Gaschütz (1954) proved that a finite group $G$ has a faithful irreducible complex representation if and only if its socle is generated by a single element as a normal subgroup; this result extends to arbitrary fields of characteristic $p$ so long as $G$ has no nontrivial normal $p$-subgroup. Žmud$'$ (1956) showed that the minimum number of irreducible constituents in a faithful complex representation of $G$ coincides with the minimum number of generators of its socle as a normal subgroup; this result can also be extended to arbitrary fields of any characteristic $p$ such that $G$ has no nontrivial normal $p$-subgroup (i.e., over which $G$ admits a faithful completely reducible representation). Rhodes (1969) characterized the finite semigroups admitting a faithful irreducible representation over an arbitrary field as generalized group mapping semigroups over a group admitting a faithful irreducible representation over the field in question. Here, we provide a common generalization of the theorems of Žmud$'$ and Rhodes by determining the minimum number of irreducible constituents in a faithful completely reducible representation of a finite semigroup over an arbitrary field (provided that it has one). Our key tool for the semigroup result is a relativized version of Žmud$'$'s theorem that determines, given a finite group $G$ and a normal subgroup $N\lhd G$, what is the minimum number of irreducible constituents in a completely reducible representation of $G$ whose restriction to $N$ is faithful.
Supercuspidal representations in non-defining characteristics
Jessica Fintzen
We show that a mod-$\ell$-representation of a p-adic group arising from the analogue of Yu's construction is supercuspidal if and only if it arises from a supercuspidal representation of a finite reductive group. This has been previously shown by Henniart and Vigneras under the assumption that the second adjointness holds, a statement that is not yet available in the literature.
Performance, Politics, and Historiography in and out of Time: American Responses to the Paris Commune
Loren Kruger
American echoes of the Paris Commune have been muffled by the nation’s obsession with freedom at the expense of solidarity, but performative responses to social upheaval, including drama, parades, and protests, have tested the boundaries of public space and multiple temporalities from 1871 to 2021. This article notes traces of the Commune in the writings and performances of nineteenth century American anarchists but analyzes this legacy primarily in the 2012 performance of Brecht’s The Days of the Commune (1949) at New York sites claimed by the Occupy Movement in 2011. It also uses the argument of Brecht’s contemporary Ernst Bloch for cultural action grounded in an understanding of historical disappointment to anticipates setbacks while maintaining hope for future revolution. The paper delineates five theses on the politics of time: 1) the dramatic appeal of the clean break hides the tension between gradual evolution and a sudden event that ruptures the long span of history (Badiou); 2) historiography, the narrative that turns data into evidence, challenges the illusion of objectivity and thus a simple split between timely intervention and untimely interference with the established order (Nietzsche); 3) ana-chronology, the logic of untimeliness reads contemporaneity as companionship between events and agents across different times and places (Barthes); 4) recollecting history requires acts of forgetting, which shatter the constraints of the past to meet demands of the present (Renan, Nietzsche); 5) the politics of time entails the politics of place and thus requires the analysis of multiple temporalitieslayered on one site as well as political acts and performance in distinct places.
Dramatic representation. The theater, The performing arts. Show business
Por uma escuta da arte: ensaio sobre poéticas possíveis na pesquisa
Rosa Maria Bueno Fischer
Neste ensaio, discute-se a possibilidade metodológica de realizar pesquisas, tendo como referência processos criativos em artes. A pergunta é: como valorizar a experimentação, as anotações do trabalho em curso, o registro dos lampejos de vida, sem perder o rigor do debate teórico, nem o olhar atento sobre urgências, éticas e políticas do presente? Com o apoio em Foucault, Hadot, Benjamin, entre outros, percorrem-se tópicos da obra do cineasta Kiarostami, de Clarice Lispector, do escritor Italo Calvino e da coreógrafa Pina Bausch. Com esses e outros exemplos, inclusive com o relato do percurso de uma pesquisa, propõem-se modos de raciocinar poeticamente, com a apropriação sem medo daquilo que ensinam diferentes artes.
Drama, Dramatic representation. The theater
Documentary on the process of creation in dance: history(ies) and memory(ies) of the body in movement
Cristiane do Rocio Wosniak
This article intend to think on a singular perspective of historical production of/about dance. It is from an interdisciplinary relationship, which involves dance and cinema, that the documentary A Alma do Gesto (2020) is take as an axis and empirical object of investigation in order to analyze creation processes in a dance company as the production of a narrative memorial on gesture and body in motion mediated by digital technology. This study draws on authors who deal with process criticism, memorial archives, history, documentaries and mise-en-scène as a basis for rethinking and deduce that, here, primary documentary sources are crossed by dance fiction.
Drama, Dramatic representation. The theater
The Im/possible Femininity of Nina Arsenault: theatrical gender in I w@s B*rbie and The Silicone Diaries
Stephen Low
This essay argues that the performed corporeality of performance artist Nina Arsenault demonstrates how gender can be constituted by two mutually exclusive theories of gender simultaneously. Specifically, Arsenault im/possibly embodies gender as performative and as an essential psychic sense of self. Her expression of a feminine identity onstage is incompatible with theories of gender performativity because it incorporates a voluntary act: performance in the theatre. Arsenault also opposes theories that claim gender is an essential psychic sense of self by expressing her sense of self in her art practice/everyday life. Arsenault highlights that the theatrical materiality she embodies, which also further establishes her femininity, is im/possibly performatively constituted. Put simply, Arsenault embodies gender through performance and performativity.
Drama, Dramatic representation. The theater
On topological representation theory from quivers
Fang Li, Zhihao Wang, Jie Wu
et al.
In this work, we introduce {\em topological representations of a quiver} as a system consisting of topological spaces and its relationships determined by the quiver. Such a setting gives a natural connection between topological representations of a quiver and diagrams of topological spaces. First, we investigate the relation between the category of topological representations and that of linear representations of a quiver via $P(Γ)$-$\mathcal{TOP}^o$ and $kΓ$-Mod, concerning (positively) graded or vertex (positively) graded modules. Second, we discuss the homological theory of topological representations of quivers via $Γ$-limit $Lim^Γ$ and using it, define the homology groups of topological representations of quivers via $H_n$. It is found that some properties of a quiver can be read from homology groups. Third, we investigate the homotopy theory of topological representations of quivers. We define the homotopy equivalence between two morphisms in $\textbf{Top}\mathrm{-}\textbf{Rep}Γ$ and show that the parallel Homotopy Axiom also holds for top-representations based on the homotopy equivalence. Last, we mainly obtain the functor $At^Γ$ from $\textbf{Top}\mathrm{-}\textbf{Rep}Γ$ to $\textbf{Top}$ and show that $At^Γ$ preserves homotopy equivalence between morphisms. The relationship is established between the homotopy groups of a top-representation $(T,f)$ and the homotopy groups of $At^Γ(T,f)$.
Lift of the trivial representation to a nonlinear double cover
Wan-Yu Tsai
Let $\widetilde G$ be the nonlinear double cover of the real points of a connected, simply connected, semisimple complex group. In [Ts], we introduce a set of genuine small representations of $\widetilde G$ with infinitesimal character $λ$, denoted $\prod _λ^s (\widetilde G)$. In this paper, we show that $\prod _{ρ/2} ^s (\widetilde G)$ is precisely the set of genuine irreducible representations arising from the Kazhdan-Patterson lifting of the trivial representation, when $\widetilde G$ is simply laced and split.
Historia żółtej ciżemki – architectural space seen through the child’s eye
Barbara Świt-Jankowska
This article focuses on the interdependencies between the film images and architectural education of the youngest. The author has attempted to define what sort of background preconditions the film image to gain the status of a source for psychoeducation, with particular emphasis placed on spatial education. The article includes a case study of Sylwester Chęciński’s film: Historia żółtej ciżemki [The Story of a Yellow Crakow] (1962).
Photography, Dramatic representation. The theater
Continuous quivers of type A (I) Foundations
Kiyoshi Igusa, Job D. Rock, Gordana Todorov
We generalize type $A$ quivers to continuous type $A$ quivers and prove initial results about pointwise finite-dimensional (pwf) representations. We classify the indecomosable pwf representations and provide a decomposition theorem, recovering results of Botnan and Crawley-Boevey. We also classify the indecomposable pwf projective representations. Finally, we prove that many of the properties of finite-dimensional type $A_n$ representations are present in finitely generated pwf representations. This is the self-contained foundational part of a series of works to study a generalization of continuous clusters categories and their relationship to other type $A$ cluster structures.
Distinguished regular supercuspidal representations
Chong Zhang
Based on recent work of Kaletha, we apply Hakim--Murnaghan's result to study distinguished regular supercuspidal representations of tamely ramified reductive $p$-adic groups. Assuming $p$ is sufficiently large, we obtain a necessary and sufficient condition for regular supercuspidal representations to be distinguished. We also investigate the relation between the distinction problem and the Langlands functoriality, and confirm a conjecture of Lapid for regular depth-zero or epipelagic supercuspidal representations.