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Tagged with hecke-algebras reference-request
12 questions
7
votes
2
answers
946
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Reference of J.L. Waldspurger's paper on Shimura correspondence
I want to find reference of Waldspurger's paper referred at "Sur les coefficients de Fourier des formes modulaires de poids demi-entier" J. Math. Pures Appl. (9) 60 (1981), no. 4, 375–484 (...
- 73
4
votes
1
answer
355
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Volumes of double cosets $KtK$
Let $G$ be the group of rational points of a connected reductive group $\mathbb G$ defined over a non-archimedean local field $F$. For simplicity sake, I assume that $\mathbb G$ is split over $F$. Let ...
- 6,349
5
votes
2
answers
545
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Basic theorem on induction for representations of $p$-adic groups
I know a lot of places where the following is sparsely proved, but I remember there was some paper where I read it in basically the same form I write it, but unfortunately I can't remember where it ...
- 463
18
votes
2
answers
1k
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What is the archimedean Hecke algebra?
Let $\mathbf G$ be a connected, reductive group over $\mathbb Q$. For each nonarchimedean place $v$, let $K_v$ be a maximal compact subgroup of $\mathbf G(\mathbb Q_v)$. The space $\mathscr H(\mathbf ...
- 6,180
7
votes
0
answers
202
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What is the kernel of the action of the Iwahori-Hecke algebra?
The Iwahori-Hecke algebra $H_n(q)$ acts on the $n$th tensor power of the standard representation of $U_q(\mathfrak{sl}_m)$. What is the kernel of this action? Does anyone know a reference?
I'm happy ...
- 425
3
votes
0
answers
72
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Reference request: Hecke agebra over non-commutative rings
I think the title sums it up quite well: Is it a useful idea to define the Iwahori-Hecke algebra over a non-commutative $k$-algebra? If so, what shape should the relations attain?
Bonus question: ...
- 281
4
votes
0
answers
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
votes
1
answer
887
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Reference request for $pro-p$ Iwahori subgroup of $GL_n(F)$
I am searching for a book/lecture notes/articles where I can find the definition and properties of the $pro-p$ Iwahori subgroup of $GL_n(F)$,(with examples if possible) the Iwahori decomposition of ...
- 685
15
votes
1
answer
759
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How many traces are there on Temperley-Lieb, Fuss-Catalan, Iwahori-Hecke, Birman-Wenzl-Murakami-Kauffman, ... algebras?
There is a theorem (I believe by Ocneanu) that the Markov trace on the tower of Temperley-Lieb algebras is (essentially) unique.
What about just traces on separate algebras? That is, take one of them,...
- 18.4k
10
votes
0
answers
430
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A question about multiplication in $G(\mathbb{C}((t)))$ and Affine Grassmannians
I am sorry to give a bounty to such a crappy question but an answer would help me a lot.
I am stuck with the following simple (i guess but) technical problem.
Let $G$ be a complex reductive ...
- 2,554
11
votes
2
answers
606
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Temperley-Lieb algebras for other Weyl groups?
The Temperley-Lieb algebra has the same generators as the $S_n$ group algebra, and the same commuting relations, but its other relations are different. A nice diagrammatic interpretation can be seen ...
- 27.8k
1
vote
1
answer
665
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Reference for Hecke algebra version of Young's orthogonal basis
In the paper Seminormal representations of Weyl groups and Iwahori-Hecke algebras, Arun Ram defines a seminormal basis as follows:
given a chain of split semisimple $K$-algebras $K\cong H_0 \subseteq ...
- 1,021