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 of mixed characteristic). For each of these topics, we obtain natural generalizations of the well-known results for connected reductive groups.
Publication Source (Journal or Book title)
Achar, P., Hardesty, W., & Riche, S. (2020). Representation Theory of Disconnected Reductive Groups. Documenta Mathematica, 25 (None), 2149-2177. https://doi.org/10.25537/dm.2020v25.2149-2177