# Tagged Questions

**3**

votes

**1**answer

91 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

**2**answers

217 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 $G$ ...

**2**

votes

**0**answers

241 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 ...

**7**

votes

**1**answer

929 views

### An interesting double coset in the theory of automorphic forms

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 $F$ , $H=GL_{n-1}$ ...

**6**

votes

**2**answers

429 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 $G:=\mathrm{SL}_n(\mathbf{Z}_p)$ ...