All Questions
3 questions
14
votes
0
answers
378
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A hard Lefschetz theorem for nilCoxeter algebras
Let $W$ be a finite Coxeter group and $\mathcal{N}(W)$ its nilCoxeter
algebra (over the reals, say), as defined at
https://en.wikipedia.org/wiki/Nil-Coxeter_algebra. $\mathcal{N}(W)$ has
a natural ...
4
votes
1
answer
171
views
Are descents in alternating subgroup counted by $h$-vector?
Consider the alternating subgroup $A_n$ of the symmetric group $S_n$ (or in general any Coxeter Group). Is there a simplicial complex whose $h$-vector $h_i$ equals the number of elements of $A_n$ with ...
1
vote
1
answer
155
views
The least common multiple of all degrees of a finite Coxeter group and indecomposable elements in the generalized cycle decomposition
This question is a follow-up of the previous question and especially the last comment therein.
Let $(W,S)$ be a finite Coxeter system with reflections $T$. Let $\ell_T$ be the reflection length. ...