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arXiv · 1002.0829

On the support varieties of Demazure modules

Benjamin F. Jones·Daniel K. Nakano
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Abstract

We consider the support varieties of Demazure modules, certain $B$-modules important in the representation theory of reductive groups. In many cases we are able to compute these support varieties over $B_1$, the first Frobenius kernel of a Borel subgroup, and relate them to orbital varieties. We provide a complete calculation of the support varieties when the underlying algebraic group has type $A_1$ or $A_2$. We also consider the saturation ($G$ orbit of) $B_1$ support varieties for Demazure modules and show that the inclusion relations among these varieties are compatible with the Bruhat order.

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Benjamin F. Jones, Daniel K. Nakano. 2011-09-14. On the support varieties of Demazure modules. https://arxiv.org/abs/1002.0829

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