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Irreducible modules for pseudoreductive groups

Banff International Research Station for Mathematical Innovation and Discovery

For any smooth connected group G over an arbitrary field k, the irreducible modules are in 1-1 correspondence with those of the pseudo-reductive quotient G/R_{u,k}(G) where R_{u,k}(G) is the k-defined unipotent radical of G. If k is imperfect, a pseudo-reductive group may not be reductive. That means that over the algebraic closure of k, one sees more unipotent radical. If G has a split maximal torus, much of the theory of split reductive groups carries over and we give dimension formulae for irreducible G-modules which reduce the study to the split reductive case and commutative pseudo-reductive case.

Mathematics; Group theory and generalizations; Geometry; Algebraic structures

video/mp4

Author affiliation: Newcastle University

2020-02-25

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/73599

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/