Irreducible modules for pseudo-reductive groups
Representation Theory
2019-11-19 v3 Group Theory
Abstract
We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive groups to the split reductive case and the pseudo-split pseudo-reductive commutative case. Moreover, we give the first results on the latter, including a rather complete description of the rank one case.
Keywords
Cite
@article{arxiv.1712.04370,
title = {Irreducible modules for pseudo-reductive groups},
author = {Michael Bate and David I. Stewart},
journal= {arXiv preprint arXiv:1712.04370},
year = {2019}
}
Comments
To appear in JEMS; significant error noted by referee and corrected from previous version: Lemma 3.1 wrongly claimed Q_G(\lambda) was M-isotypic; see Rk 7.4(ii) in this version