All Questions
Tagged with hecke-algebras ra.rings-and-algebras
8 questions
4
votes
1
answer
142
views
Property of simplicity and semi-simplicity under base change of base field
Suppose $K$ is a field of characteristic $0$ and $A$ is a $K$-algebra. Let $F$ be a field extension of $K$ and let $M$ be an $A$-module. What can we say about simplicity or semi-simplicity of $A_F$-...
1
vote
1
answer
190
views
Commutative subalgebra of Iwahori-Hecke algebra
I am currently reading the (french) book [1] by Matsumoto. In (2.1.11) the following statement (reformulated in my own words/notation) appears:
Let $(W,S)$ be a Coxeter system, let $R$ be a ...
- 741
2
votes
1
answer
254
views
Noncommutative cohomology of flag varieties
Consider the Grassmannian $Gr(n, N)$ of $n$-dimensional subspaces of $\mathbf C^N$. Its cohomology ring is isomorphic to $\mathbf C[x_1, \ldots, x_n, \bar x_1, \ldots \bar x_{N-n}]/I_{n,N}$, wherethe ...
- 281
15
votes
1
answer
759
views
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
11
votes
2
answers
606
views
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
14
votes
2
answers
1k
views
Name for algebra and its tensor products
Is there a name for the algebra (and its tensor products) given by generators $M_{j}$, $j \in \mathbb{Z}_{n}$ under the conditions $$M_{j} = (1 - M_{j-1})(1-M_{j+1})$$ where $j=1\implies j-1=n$ and $j=...
- 13.9k
7
votes
2
answers
692
views
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 ...
- 303
4
votes
2
answers
1k
views
Difference between orthogonal form and seminormal form
Frequently in the literature on Hecke algebras for the symmetric group and their generalisations, one encounters references to Young's seminormal form and Young's orthogonal form. I have a good ...
- 159