Questions tagged [hecke-algebras]
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12 questions
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Definitions of Hecke algebras
There is a definition of Iwahori-Hecke algebras for Coxeter groups in terms of generators and relations and there is a definition of Hecke algebras involving functions on locally compact groups. Are ...
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Are there Hamilton paths in Cayley graphs of Coxeter groups?
Hi everyone.
I want to optimize certain computation on finite Coxeter groups $(W,S)$. Basically I compute the matrices $\rho(T_w)$ for all $w\in W$ of a matrix representation $H\to K^{d\times d}$ of ...
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Index of the Hecke algebra with operators omitted
This is a spin-off to the question Omitting primes from a Hecke algebra by David Loeffler.
Let $N$ be a positive integer. For a finite set of primes $\Sigma$, let $\mathbb T^{\Sigma}$ be the $\mathbb ...
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Why are there no triple affine Hecke algebras?
This question arised after I recently stumbled upon the paper "Triple groups and Cherednik algebras". Doubly affine Hecke algebras are sort of a natural object to consider after finite and affine ...
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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,...
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Hecke Operators for $\Gamma_1(N)$ *with* character?
Hello.
I wonder whether there are hecke operators for modular forms for $\Gamma = \Gamma_1(N)$ with additive character $\chi : \mathbb{Z}_N \mapsto \mathbb{C}^{\times}$. There is a somewhat ...
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Bernstein's presentation for the Hecke algebra
Any one know of any good references for reading about Bernstein's presentation of the Iwahori Hecke algebra? I need some notes which has an example or two. It would really help.
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Are these two subspaces of $\mathbb{Z}/2[[x]]$ the same?
The following questions arise from modular form theory. But this theory isn't needed to formulate or understand them, and I'm not using the modular-forms tag.
NOTATION
Fix an odd prime $N$. Let
$$
...
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Relation between Hecke operators and coefficient of L-functions
This question has its seed in this one by Gory, which found an enlightening answer but one of the comments kept me wondering. I am beginning to discover Hecke operators, and there appears to be an ...
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Is $(G\rtimes H,H)$ a Gelfand pair iff $G$ is abelian?
Let $G$ be a finite group and $K \subset G$ a subgroup. Then $(G,K)$ is a Gelfand pair if the double coset Hecke algebra $\mathbb{C}(K \backslash G / K)$ is commutative.
Let $H$ be a subgroup of $...
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Two spaces attached to mod 2 level 9 modular forms--a conjectural Hecke isomorphism
MOTIVATION
Nicolas and Serre have analyzed the structure of the space of mod $2$ modular forms of level $1$, viewed as a "Hecke-module". They show that for each $p>2$, the operator $T_p$ acting on ...
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Degenerate affine Hecke Algebra
What are the generators of the degenerate affine Hecke algebra $H(k)$ for $k > 0$?
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