New answers tagged coxeter-groups
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What is known about finite dimensional modules over the nilCoxeter algebra?
Motivated by the answers I tried to check when it is symmetric and I got the result that it symmetric is if and only if conjugation by the longest element acts as the identity in the corresponding ...
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What is known about finite dimensional modules over the nilCoxeter algebra?
@DaveBenson, has already given a beautiful answer to this question. I just wanted to point out that a number of the things he says (although not his full computation of the dimension of the Ext-...
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Accepted
What is known about finite dimensional modules over the nilCoxeter algebra?
This algebra has just one isomorphism class of simple module - let's call it $S$. Its projective cover is the regular representation, and is also the injective hull. The socle of the regular ...
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coset poset of reflection subgroup
I assume that $W$ is finit (not just $S$) and I take parabolic subgroups rather than reflection subgroups. Then the coset poset is indeed Cohen-Macaulay.
In the recent work Cluster Parking Functions, ...
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