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Journal Articles Documenta Mathematica Year : 2020

Representation theory of disconnected reductive groups

Abstract

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.
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hal-01897282 , version 1 (17-10-2018)

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Pramod N. Achar, William Hardesty, Simon Riche. Representation theory of disconnected reductive groups. Documenta Mathematica, 2020, 25, pp.2149-2177. ⟨hal-01897282⟩
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