Representation theory of disconnected reductive groups

Pramod N. Achar (1) , William Hardesty (1) , Simon Riche (2, 3)

1 LSU Mathematics - Department of Mathematics [Baton Rouge]
2 LMBP - Laboratoire de Mathématiques Blaise Pascal
3 UCA [2017-2020] - Université Clermont Auvergne [2017-2020]

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.

Domaines: Théorie des représentations [math.RT]

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