arXiv subjects

S. Riche

Publications and source records attributed to S. Riche.

2 recordsLinked to original sources

arXiv2020

Modular affine Hecke category and regular unipotent centralizer

In this paper we provide, under some mild explicit assumptions, a geometric description of the category of representations of the centralizer of a regular unipotent element in a reductive algebraic group in terms of perverse sheaves on the Langlands dual affine flag variety. This equivalence is suggested and motivated by the "geometric Langlands" philosophy, and is used in later work to construct equivalences of categories relating various geometric incarnations of the affine Hecke algebra of the given reductive group.

math.RT↗

arXiv2018

Representation theory of disconnected reductive groups

We study three fundamental topics in the representation theory of disconnected algebraic groups whose identity component is reductive: (i) the classification of irreducible representations; (ii) the existence and properties of Weyl and dual Weyl modules; and (iii) the decomposition map relating representations in characteristic $0$ and those in characteristic $p$ (for groups defined over discrete valuation rings). For each of these topics, we obtain natural generalizations of the well-known results for connected reductive groups.

math.RT↗