10
votes
1answer
276 views

Does the 'string property' finish Joseph's proof of Demazure character formula?

The too long, didn't read form of the question would simply be, has someone completed A. Joseph's proof of the Demazure character formula? Is Joseph's proof considered complete? In more detail, ...
11
votes
0answers
289 views

Is there a notion of tensor product of perfect bases of representations of Lie algebras?

Berenstein and Kazhdan define perfect bases as an "unquantized" version of crystal bases. A perfect basis is roughly a basis with a crystal structure such that $E_i\cdot v=\mathbb{C}\cdot ...
5
votes
1answer
248 views

Are there elements of fixed weight in a crystal not killed by too many Kashiwara operators?

I've come across an annoying lemma trying to finish up an argument, and I was hoping one of you guys knew about it. Question: Given a weight $\lambda$ of a simple Lie algebra $\mathfrak g$, and ...