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Description

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.