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Results tagged with hecke-algebras
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user 919
8
votes
Positivity of Iwahori–Hecke algebra characters on the Kazhdan-Lusztig basis
This is a really good question. What is known of an answer is somewhat
complicated, and perhaps others have more useful things to say.
As you mention, the Hecke algebra $H$ is categorified by the Heck …
- 6,162
3
votes
Accepted
Parabolic convolution of perverse sheaves in terms of the Hecke algebra
Let $G$ be a connected reductive algebraic group (over $\mathbb{C}$) and fix a Borel subgroup $B \subset G$. One can consider the 2-category with objects parabolic subgroups $P \supset B$ and 1-morphi …
- 6,162
25
votes
Is Soergel's proof of Kazhdan-Lusztig positivity for Weyl groups independent of other proofs?
Perhaps I can supplement Jim's answer a little.
In the paper "Kazhdan-Lusztig-Polynome und unzerlegbare Bimoduln uber Polynomringen" Soergel shows that there are certain graded indecomposable bimodul …
- 6,162
4
votes
Subexpressions of reduced words in Coxeter groups
I have found a much more efficient way of solving this problem on computer. Having asked the question I guess I should provide a brief account. However I feel like the algorithm is technical and not v …
- 6,162
9
votes
2
answers
894
views
Subexpressions of reduced words in Coxeter groups
Let $\underline{w} = [s_1, s_2, \dots ,s_n]$ be a reduced expression in a Coxeter group $W$. Given $x$ in $W$ one can consider the set $\Pi(\underline{w},x)$ consisting of all subexpressions of $\unde …
- 6,162