Representation Theory of Disconnected Reductive Groups
Pramod N. AcharDepartment of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA
William D. HardestySchool of Mathematics and Statistics F07, University of Sydney, NSW 2006, Australia
Simon RicheUniversité Clermont Auvergne CNRS, LMBP, F-63000 Clermont-Ferrand, France
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.
Cite this article
Pramod N. Achar, William D. Hardesty, Simon Riche, Representation Theory of Disconnected Reductive Groups. Doc. Math. 25 (2020), pp. 2149–2177DOI 10.4171/DM/796