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Results tagged with coxeter-groups
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user 919
A Coxeter group is a group defined by a presentation by involutions $r_i$ with relators $(r_ir_j)^{m_{ij}}=1$ for certain family $(m_{ij})$ of integers greater than 1.
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
12
votes
Accepted
Intrinsic characterization of Soergel bimodules?
There is an intrinsic characterisation which is probably more complicated than what you are looking for. As Ben says, Soergel bimodules are pretty subtle things ...
Because Soergel bimodules are (fin …
- 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
4
votes
Accepted
Are parabolic Kazhdan-Lusztig polynomials truncations of the usual Kazhdan-Lusztig polynomials?
A quick answer for which standard health warnings apply.
For your first question, the answer is positive, as follows (for example) from my paper with Libedinsky here: https://arxiv.org/abs/1702.00459
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