All Questions
Tagged with reductive-groups hecke-algebras
8 questions
5
votes
2
answers
430
views
Parabolic induction, and tensoring (Iwahori/affine) Hecke algebras
In several places, such as [1] and [2], it seems to be implicitly known that (normalized) parabolic induction corresponds to tensoring affine Hecke algebras. I say implicitly because both [1] and [2] ...
3
votes
0
answers
103
views
compactly induction of smooth modules over Hecke algebras
Let $G$ be a locally profinite group and $H$ its closed subgroup. It is well-known that a smooth representation of $G$ is identified with a smooth module over $\mathcal{H}(G)$, where $\mathcal{H}(G)$ ...
- 479
6
votes
1
answer
500
views
Cusp forms have an orthonormal basis of eigenfunctions for all Hecke operators
I am reading Langlands' pape Euler Products and have a few questions. Let $G$ be a split adjoint semisimple group over $\mathbb Q$. If $p$ is a place of $\mathbb Q$, finite or infinite, let $G_{\...
- 6,180
4
votes
1
answer
355
views
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
18
votes
2
answers
1k
views
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
4
votes
1
answer
887
views
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
2
votes
2
answers
570
views
description of an endomorphism algebra
Let $G$ be a reductive group, $F$ a Frobenius morphism, $B$ a Borel subgroup $F$-stable and consider the finite groups $G^F$ and $U^F$ where $U$ is the radical unipotent of $B=UT$ ($T$ torus).
I ...
- 311
1
vote
1
answer
249
views
Algorithm for the cell multiplication rule for GL(n,F)
Consider $F$ a non archimedean field and let $o$ be its ring of integer
Let $B$ be the Iwahori subgroup of $GL_n(F)$ (resp. $GL_n(o)$) and let $N$ be the normalizer of the diagonal matrices (...
- 11.2k