3
votes
1answer
80 views

Siegel domains and cuspidal functions

Let $F$ be a number field and $\mathbb{A}$ the ring of adeles over $F$. We consider $P_{n}$ the mirabolic subroup of $GL_{n}$. Do we have a analog of Siegel subset for the quotient ...
3
votes
2answers
204 views

Restriction map between spaces of automorphic forms

Hello, Let $H \subset G$ be reductive groups defined over $\mathbb{Q}$. I consider the spaces of automorphic forms of $G$ and $H$. One has a restriction map from the space of automorphic forms of $G$ ...
1
vote
0answers
232 views

on the fundamental lemma

I consider the fundamental lemma for the spherical Hecke algebra. Let $G$ a connected reductive quasisplit group on $F$, a local field of equal characteristic $p$. and $H$ an endoscopic group. Can ...
5
votes
1answer
729 views

An interesting double coset in the theory of automorphic forms

Dear all, Does anyone have some idea to describe the double coset $P(F)\\backslash G(F)/H(F)$ , say using Weyl group elements ? Here $G=GL_n\times GL_{n-1}$ is defined over a number field $F$ , ...
6
votes
2answers
428 views

Orbits of SL_n acting on matrices of determinant p

Fix a positive integer $n$ and let $S$ be the set of $n$ by $n$ matrices with entries in $\mathbf{Z}_p$ (the $p$-adic integers) whose determinant is $p$. The group $G:=\mathrm{SL}_n(\mathbf{Z}_p)$ ...