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Answer by Tiago for On q-Demazure operators

Dear Chuck Hague,It may not answer your question. But let me suggest you to take a look at sections 4.5, 5.3 and 5.4 of:A. Joseph, Modules with a Demazure flag. Studies in Lie theory, 131–169, Progr....

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On q-Demazure operators

SetupLet $G$ be a semisimple algebraic group over an algebraically closed field of arbitrary characteristic with Borel subgroup $B$. Let $\Lambda$ denote the weight lattice of $G$; we write elements of...

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