Formal degree and existence of stable arithmetic lattices of cuspidal representations ofp-adic reductive groups

1989 ◽  
Vol 98 (3) ◽  
pp. 549-563
Author(s):  
M. F. Vigneras
Keyword(s):  
Reductive Groups ◽  
Formal Degree ◽  
Cuspidal Representations

scholarly journals ON A CERTAIN LOCAL IDENTITY FOR LAPID–MAO'S CONJECTURE AND FORMAL DEGREE CONJECTURE : EVEN UNITARY GROUP CASE

2021 ◽  
pp. 1-55
Author(s):  
Kazuki Morimoto
Keyword(s):  
Explicit Formula ◽  
Unitary Group ◽  
Fourier Coefficients ◽  
Automorphic Forms ◽  
Unitary Groups ◽  
Reductive Groups ◽  
Local Identity ◽  
Metaplectic Groups ◽  
Group Case ◽  
Formal Degree

Abstract Lapid and Mao formulated a conjecture on an explicit formula of Whittaker–Fourier coefficients of automorphic forms on quasi-split reductive groups and metaplectic groups as an analogue of the Ichino–Ikeda conjecture. They also showed that this conjecture is reduced to a certain local identity in the case of unitary groups. In this article, we study the even unitary-group case. Indeed, we prove this local identity over p-adic fields. Further, we prove an equivalence between this local identity and a refined formal degree conjecture over any local field of characteristic zero. As a consequence, we prove a refined formal degree conjecture over p-adic fields and get an explicit formula of Whittaker–Fourier coefficients under certain assumptions.

scholarly journals STEENROD OPERATIONS ON THE DE RHAM COHOMOLOGY OF ALGEBRAIC STACKS

2021 ◽  
pp. 1-48
Author(s):  
Federico Scavia
Keyword(s):  
Finite Groups ◽  
Reductive Groups ◽  
Orthogonal Groups ◽  
De Rham Cohomology ◽  
Algebraic Stacks ◽  
Steenrod Operations ◽  
De Rham

Abstract Building upon work of Epstein, May and Drury, we define and investigate the mod p Steenrod operations on the de Rham cohomology of smooth algebraic stacks over a field of characteristic $p>0$ . We then compute the action of the operations on the de Rham cohomology of classifying stacks for finite groups, connected reductive groups for which p is not a torsion prime and (special) orthogonal groups when $p=2$ .

Symplectic slices for actions of reductive groups

2006 ◽  
Vol 197 (2) ◽  
pp. 213-224
Author(s):  
I V Losev
Keyword(s):  
Reductive Groups

scholarly journals Alvis–Curtis duality for representations of reductive groups with Frobenius maps

2020 ◽  
Vol 32 (5) ◽  
pp. 1289-1296
Author(s):  
Junbin Dong
Keyword(s):  
Irreducible Representations ◽  
Reductive Groups ◽  
Infinite Type ◽  
Abstract Representations

AbstractWe generalize the Alvis–Curtis duality to the abstract representations of reductive groups with Frobenius maps. Similar to the case of representations of finite reductive groups, we show that the Alvis–Curtis duality of infinite type, which we define in this paper, also interchanges the irreducible representations in the principal representation category.

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.

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