JournalsdmVol. 25pp. 2149–2177

Representation Theory of Disconnected Reductive Groups

  • Pramod N. Achar

    Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA

  • William D. Hardesty

    School of Mathematics and Statistics F07, University of Sydney, NSW 2006, Australia

  • Simon Riche

    Université Clermont Auvergne CNRS, LMBP, F-63000 Clermont-Ferrand, France
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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 and those in characteristic (for groups defined over discrete valuation rings of mixed characteristic). For each of these topics, we obtain natural generalizations of the well-known results for connected reductive groups.

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Pramod N. Achar, William D. Hardesty, Simon Riche, Representation Theory of Disconnected Reductive Groups. Doc. Math. 25 (2020), pp. 2149–2177

DOI 10.4171/DM/796