Filtrations of rational representations of reductive groups of semisimple rank 1

Doty, Stephen

doi:10.1090/S0002-9939-1990-1000153-4

Filtrations of rational representations of reductive groups of semisimple rank $1$
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Proc. Amer. Math. Soc. 109 (1990), 9-22 Request permission

Abstract:

A detailed study is made of the affine coordinate ring of the Chevalley group ${\text {S}}{{\text {L}}_2}$ over the integers as base ring. Certain applications to the representation theory of groups of semisimple rank 1 are made, including the construction of a filtration on modules obtained by inducing a character of a maximal torus $T$ from $T$ up to the group. We show this filtration extends the Jantzen-Andersen filtration on the dual Weyl module with highest weight given by that character, in case the character in question is dominant.

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