scholarly journals Coproduct for affine Yangians and parabolic induction for rectangular W-algebras

2022 ◽  
Vol 112 (1) ◽  
Author(s):  
Ryosuke Kodera ◽  
Mamoru Ueda
Keyword(s):  
Parabolic Induction

scholarly journals On Reducibility and Unitarizability for Classical p-Adic Groups, Some General Results

2009 ◽  
Vol 61 (2) ◽  
pp. 427-450 ◽  
Author(s):  
Marko Tadić
Keyword(s):  
Reductive Groups ◽  
Parabolic Induction

Abstract. The aim of this paper is to prove two general results on parabolic induction of classical p-adic groups (actually, one of them holds also in the archimedean case), and to obtain from them some consequences about irreducible unitarizable representations. One of these consequences is a reduction of the unitarizability problem for these groups. This reduction is similar to the reduction of the unitarizability problem to the case of real infinitesimal character for real reductive groups.

scholarly journals Geometric approach to parabolic induction

2016 ◽  
Vol 22 (4) ◽  
pp. 2243-2269 ◽  
Author(s):  
David Kazhdan ◽  
Yakov Varshavsky
Keyword(s):  
Geometric Approach ◽  
Parabolic Induction

scholarly journals Sur les -blocs de niveau zéro des groupes -adiques

2018 ◽  
Vol 154 (7) ◽  
pp. 1473-1507
Author(s):  
Thomas Lanard
Keyword(s):  
Abelian Category ◽  
Langlands Correspondence ◽  
Parabolic Induction ◽  
Langlands Parameters ◽  
Tits Building ◽  
Local Langlands Correspondence

Let $G$ be a $p$-adic group that splits over an unramified extension. We decompose $\text{Rep}_{\unicode[STIX]{x1D6EC}}^{0}(G)$, the abelian category of smooth level $0$ representations of $G$ with coefficients in $\unicode[STIX]{x1D6EC}=\overline{\mathbb{Q}}_{\ell }$ or $\overline{\mathbb{Z}}_{\ell }$, into a product of subcategories indexed by inertial Langlands parameters. We construct these categories via systems of idempotents on the Bruhat–Tits building and Deligne–Lusztig theory. Then, we prove compatibilities with parabolic induction and restriction functors and the local Langlands correspondence.

scholarly journals Conjectures and results about parabolic induction of representations of $${\text {GL}}_n(F)$$

2020 ◽  
Vol 222 (3) ◽  
pp. 695-747
Author(s):  
Erez Lapid ◽  
Alberto Mínguez
Keyword(s):  
Linear Group ◽  
Local Field ◽  
General Linear Group ◽  
Irreducible Representations ◽  
General Linear ◽  
Parabolic Induction ◽  
Geometric Conditions ◽  
Irreducible Components ◽  
Special Cases

Abstract In 1980 Zelevinsky introduced certain commuting varieties whose irreducible components classify complex, irreducible representations of the general linear group over a non-archimedean local field with a given supercuspidal support. We formulate geometric conditions for certain triples of such components and conjecture that these conditions are related to irreducibility of parabolic induction. The conditions are in the spirit of the Geiss–Leclerc–Schröer condition that occurs in the conjectural characterization of $$\square $$ □ -irreducible representations. We verify some special cases of the new conjecture and check that the geometric and representation-theoretic conditions are compatible in various ways.

scholarly journals Parabolic induction and Jacquet functors for metaplectic groups

2010 ◽  
Vol 323 (1) ◽  
pp. 241-260 ◽  
Author(s):  
Marcela Hanzer ◽  
Goran Muić
Keyword(s):  
Metaplectic Groups ◽  
Parabolic Induction

scholarly journals ADJOINT FUNCTORS BETWEEN CATEGORIES OF HILBERT -MODULES

2016 ◽  
Vol 17 (2) ◽  
pp. 453-488 ◽  
Author(s):  
Pierre Clare ◽  
Tyrone Crisp ◽  
Nigel Higson
Keyword(s):  
Category Theory ◽  
Reductive Groups ◽  
Hilbert Modules ◽  
Adjoint Functors ◽  
Left Action ◽  
Parabolic Induction ◽  
Left And Right ◽  
Restriction Functor ◽  
Tempered Representation ◽  
Standard Concept

Let$E$be a (right) Hilbert module over a$C^{\ast }$-algebra$A$. If$E$is equipped with a left action of a second$C^{\ast }$-algebra$B$, then tensor product with$E$gives rise to a functor from the category of Hilbert$B$-modules to the category of Hilbert$A$-modules. The purpose of this paper is to study adjunctions between functors of this sort. We shall introduce a new kind of adjunction relation, called a local adjunction, that is weaker than the standard concept from category theory. We shall give several examples, the most important of which is the functor of parabolic induction in the tempered representation theory of real reductive groups. Each local adjunction gives rise to an ordinary adjunction of functors between categories of Hilbert space representations. In this way we shall show that the parabolic induction functor has a simultaneous left and right adjoint, namely the parabolic restriction functor constructed in Clareet al.[Parabolic induction and restriction via$C^{\ast }$-algebras and Hilbert$C^{\ast }$-modules,Compos. Math.FirstView(2016), 1–33, 2].

scholarly journals Springer correspondence for the split symmetric pair in type

2018 ◽  
Vol 154 (11) ◽  
pp. 2403-2425 ◽  
Author(s):  
Tsao-Hsien Chen ◽  
Kari Vilonen ◽  
Ting Xue
Keyword(s):  
Fourier Transform ◽  
Hecke Algebras ◽  
Symmetric Groups ◽  
Irreducible Representations ◽  
Symmetric Pair ◽  
Parabolic Induction ◽  
Hessenberg Varieties ◽  
Nearby Cycle ◽  
Springer Correspondence

In this paper we establish Springer correspondence for the symmetric pair $(\text{SL}(N),\text{SO}(N))$ using Fourier transform, parabolic induction functor, and a nearby cycle sheaf construction. As an application of our results we see that the cohomology of Hessenberg varieties can be expressed in terms of irreducible representations of Hecke algebras of symmetric groups at $q=-1$. Conversely, we see that the irreducible representations of Hecke algebras of symmetric groups at $q=-1$ arise in geometry.

scholarly journals Parabolic induction and restriction functors for rational Cherednik algebras

2009 ◽  
Vol 14 (3-4) ◽  
pp. 397-425 ◽  
Author(s):  
Roman Bezrukavnikov ◽  
Pavel Etingof
Keyword(s):  
Cherednik Algebras ◽  
Parabolic Induction ◽  
Rational Cherednik Algebras
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