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Irreducible modules for pseudo-reductive groups

Lookup NU author(s): Dr David Stewart



This is the authors' accepted manuscript of an article that has been accepted and is due to be published in its final definitive form by Europeon Mathematical Society Publishing House, 2020.

For re-use rights please refer to the publisher's terms and conditions.


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.

Publication metadata

Author(s): Bate M, Stewart DI

Publication type: Article

Publication status: In Press

Journal: Journal of the European Mathematical Society

Year: 2020

Acceptance date: 09/11/2019

Date deposited: 18/11/2019

ISSN (print): 1435-9855

ISSN (electronic): 1435-9863

Publisher: Europeon Mathematical Society Publishing House


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