Questions tagged [hecke-algebras]
The hecke-algebras tag has no usage guidance.
9 questions from the last 365 days
2
votes
0
answers
92
views
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
11
votes
1
answer
331
views
A question on groups having a subgroup which fixes a vector in every irreducible representations
Given a finite group $G$, I am interested in finding a non-trivial proper subgroup $H$ of $G$ such that $\mathrm{Ind}_H^G\mathbf{1}$ contains all the irreducible representations of $G$, that is, ...
- 251
2
votes
0
answers
72
views
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
2
votes
0
answers
61
views
Quiver and relations for the 0-Hecke algebra
Let $A_n=H_n(0)$ denote the 0-Hecke algebra, see for example König - $0$-Hecke algebras of the symmetric groups.
All simple $A_n$ modules are 1-dimensional and thus $A_n$ is isomorphic to an algebra ...
- 26.5k
3
votes
0
answers
72
views
How to multiply dots with Young idempotents in the degenerate affine Hecke algebra (type A)
Let $\widehat{\cal H}_n$ be the type A degenerate affine Hecke algebra on $n$ strands, and let $x_1,\cdots,x_n$ be the dots. Inside of this algebra lies the algebra $\mathbb C S_n$, and the Young ...
- 311
4
votes
0
answers
110
views
Hecke algebra $\mathcal{H}(K_1\backslash \mathrm{GL}_n(\mathbb{F})/K_1)$
$\DeclareMathOperator\GL{GL}$Let $\mathbb{F}$ be a non-Archimedean local field. Let $\mathcal{O}$ be its ring of integers, and let $\frak{m}$ be its maximal ideal Let $\GL_n(\mathcal{O})$ be the group ...
- 21.8k
10
votes
1
answer
530
views
How is Taylor-Wiles patching "horizontal Iwasawa theory"?
I have recently been reading into the proof of modularity of semistable elliptic curves, in particular (what is now known as) the Taylor-Wiles patching argument used to prove the $R=T$ theorem in the ...
- 28.2k
3
votes
0
answers
156
views
Taylor-Wiles systems for higher dimensional deformation rings
Let $R$ be a deformation ring and $M$ be a finitely generated $R$-module.
A strategy for proving the theorems $R=T$ is to associate with $(R,M)$ a Taylor-Wiles system denoted $(R_{Q},M_{Q})$. Here I'm ...
- 1,270
1
vote
0
answers
100
views
Automorphisms of Iwahori/affine Hecke algebras
Has there been any serious study of automorphisms of extended affine Hecke algebras? Has anyone determined the automorphism group of say, type A extended affine Hecke algebras? I ask because the ...