Associated varieties for real reductive groups

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 $p=2$ .

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Symplectic slices for actions of reductive groups

Sbornik Mathematics ◽

10.1070/sm2006v197n02abeh003754 ◽

2006 ◽

Vol 197 (2) ◽

pp. 213-224

Author(s):

I V Losev

Keyword(s):

Reductive Groups

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A Satake isomorphism for representations modulo p of reductive groups over local fields

Journal für die reine und angewandte Mathematik (Crelles Journal) ◽

10.1515/crelle-2013-0021 ◽

2013 ◽

Vol 0 (0) ◽

Cited By ~ 3

Author(s):

Guy Henniart ◽

Marie-France Vignéras

Keyword(s):

Local Fields ◽

Reductive Groups ◽

Modulo P ◽

Satake Isomorphism

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

Forum Mathematicum ◽

10.1515/forum-2020-0053 ◽

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.

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

Canadian Journal of Mathematics ◽

10.4153/cjm-2009-022-7 ◽

2009 ◽

Vol 61 (2) ◽

pp. 427-450 ◽

Cited By ~ 6

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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