All Questions
Tagged with hecke-algebras kazhdan-lusztig
9 questions
2
votes
0
answers
92
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Geometric interpretation of flags and the role of the rook monoid and Kazhdan–Lusztig theory in $M_n(\mathbb{C})$
Let $G = GL_n(\mathbb{C})$, $B$ be its Borel subgroup, and $P$ a parabolic subgroup. The space $G/B$ corresponds to complete flags in $ \mathbb{C}^n$, and $G/P$ corresponds to partial flags. The ...
- 141
8
votes
3
answers
635
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Motivation for the Kazhdan-Lusztig involution
I would like to know about the motivation behind the Kazhdan–Lusztig involution on an Iwahori–Hecke algebra.
I'll borrow the conventions from Libedinsky's Gentle introduction to Soergel bimodules I: ...
- 721
4
votes
1
answer
350
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Examples of non-trivial Kazhdan-Lusztig polynomials
I'm looking for examples of non-trivial Kazhdan-Lusztig polynomials, specifically in the case where the Coxeter system is a Weyl group.
For example, the simplest polynomial with non-trivial $q$-...
4
votes
1
answer
241
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Number of pairs of permutation in $S_n$ whose $\mu$-coefficient (of their Kazhdan Lusztig polynomial) is non-zero
I am interested in how many pairs of permutations $(u,w)$ in $S_n$, such that the $\mu$-coefficient of its Kazhdan-Lusztig polynomial $P_{u,w}(q)$ is non-zero? where $\mu_{u,w}=[q^{\frac{l(w)-l(u)-1}{...
1
vote
1
answer
132
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About left cell of a permutation
I am reading a paper Cellular algebras by J.J. Graham, G.I. Lehrer. I do not understand the follwing words labelled by yellow.
First, I know Robinson-Schensted correspondence of a permutation in the ...
- 331
1
vote
0
answers
32
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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
3
votes
0
answers
414
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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
4
votes
0
answers
156
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Degeneration of modules over the affine symmetric group and jeu de taquin
Let $H_n$ be the group algebra of the affine Coxeter group of type A (feel free to replace it by the affine Hecke algebra). This is generated by elements $y_i$'s, $i=1,\dots,n$ and transpositions $s_i$...
- 8,524
6
votes
1
answer
587
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When are parabolic Kazhdan-Lusztig polynomials nonzero?
Let $W$ be a Coxeter group with simple reflections $S$ and let $J \subseteq S$. Let $P^J_{\tau, \sigma}$ be the parabolic Kazhdan-Lusztig polynomials in the case $u = q$ in the sense of On Some ...
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