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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Filtrations of rational representations of reductive groups of semisimple rank $ 1$


Author: Stephen Doty
Journal: Proc. Amer. Math. Soc. 109 (1990), 9-22
MSC: Primary 20G05; Secondary 20G10, 22E45
DOI: https://doi.org/10.1090/S0002-9939-1990-1000153-4
MathSciNet review: 1000153
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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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DOI: https://doi.org/10.1090/S0002-9939-1990-1000153-4
Article copyright: © Copyright 1990 American Mathematical Society