All Questions
Tagged with coxeter-groups hecke-algebras
7 questions with no upvoted or accepted answers
20
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A spin extension of a Coxeter group?
Consider a Coxeter group $W$ with simple generators $S$ and Coxeter matrix $\left( m_{s,t}\right) _{\left( s,t\right) \in S\times S}$.
Let $\mathfrak{M}$ be the set of all pairs $\left(s, t\right) ...
- 33.8k
5
votes
0
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207
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Kazhdan-Lusztig basis elements appearing in product with distinguished involution
My apologies if the below is too malformed to make sense.
Let $(W,S)$ be the affine Weyl group of a reductive group $G$, and let $\{C_w\}$ be the Kazhdan-Lusztig $C$-basis (an answer in terms of the $...
- 413
4
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202
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Shifts in the decomposition of Bott-Samelson bimodules
Let $k$ be an algebraically closed field of characteristic $0$, let $V=k^n$ be a $k$ vector space of dimension $n$, and let $R=k[V]$ be the ring of polynomial functions on $V$. Suppose that $W\subset\...
- 868
4
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94
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Highest (short) roots and commutation relations in (twisted) DAHA
I am trying to understand, explicitly, the commutation relation between $X_\vartheta$ and $Y_\vartheta = T_0T_{s_\vartheta}$ in the (twisted) DAHA for a root system $R$, where $\vartheta$ is the ...
- 41
3
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Kazhdan-Lusztig basis of the symmetric group algebra $\mathbb{K}S_n$
Let $S_n$ be the symmetric group on the set $\{1,2,\ldots,n\}$ and $\mathbb{K}$ a field. Denote by $\mathbb{K}S_n$ the symmetric group algebra.
What's Kazhdan-Lusztig basis of $\mathbb{K}S_n$? I ...
- 331
2
votes
0
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Does this finitely-generated algebra have a name?
I've been led to consider certain finitely-generated algebras that arise from some Coxeter groups (finite and affine Weyl groups at least). As a very concrete example, consider the infinite dihedral ...
- 13.3k
1
vote
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Cellular basis of $KW(B_2)$
Take $K$ a field. Let $W(B_2)$ be the coxeter group of type $B_2$ with a set $\{s_0,s_1\}$ of generators. Then $W(B_2)=\{1, s_0,s_1,s_0s_1,s_1s_0,s_0s_1s_0, s_1s_0s_1,s_1s_0s_1s_0\}$. I know that the ...
- 331