All Questions
10 questions with no upvoted or accepted answers
9
votes
0
answers
409
views
The proof of Kazhdan's density theorem (And does it hold over positive characteristic?)
When proving identities about traces of functions on representations of $p$-adic groups, Kazhdan's density theorem indicates one only has to check equalities of traces on tempered representations. ...
- 181
6
votes
0
answers
261
views
Local character expansion for discrete series representations of $GL_n(F)$
I'm interested about what, if anything, is known about the local character expansion of discrete-series representations of $GL_n(F)$, where $F$ is a $p$-adic field.
First, some notation: let $G$ be a ...
- 1,453
4
votes
0
answers
124
views
Finite dimensional irreps of $p$-adic groups
What are some examples of finite dimensional irreducible complex representations of $SL_2(\mathbb{Q}_p)$?
One knows such a representations cannot be smooth, so probably the examples will be ...
- 81
4
votes
0
answers
135
views
Growth of the number of fixed points of a $p$-adic group under natural filtrations
Let $G$ be a $p$-adic reductive group, so by definition as a locally profinite group it's the group of $\mathbb Q_p$ points of a connective reductive group over $\mathbb Q_p$, $K$ be a parahoric ...
- 6,622
4
votes
0
answers
313
views
How to determine the unramified character corresponding to an unramified Langlands parameter?
Let $F$ be a p-adic field with ring of integers $\mathcal{O}$. Let $\textbf{G}$ be a connected split reductive algebraic group over $F$. For simplicity, we assume that $\textbf{G}$ is a Chevalley ...
- 960
4
votes
0
answers
219
views
A question of integral on $p$-adic fields $\mathbb{Q_p}$
We assume that $(\pi,V)$ is an admissible, irreducible and infinite-dimensional representation of $GL_2(\mathbb{Q_p})$. In the proof of existence and uniqueness of Kirillov model, the key step is that ...
- 421
3
votes
0
answers
101
views
Hermitian sublattices of a given type
Consider an unramified quadratic extension $E/F$ of non-archimedean local fields, and suppose that $\langle\cdot,\cdot\rangle$ is a fixed Hermitian form on $E^d$ such that $\mathcal{O}_E^d$ is self-...
- 2,516
2
votes
0
answers
169
views
$\mathrm{Ext}^i(\pi_1, \pi_2)\neq0$ implies same central character
If $\pi_1$ and $\pi_2$ are two smooth admissible representations of $\operatorname{GL}_2(\mathbb{Q}_p)$ over $\overline{\mathbb{F}}_p$ with central characters. I want to prove that if $\pi_1$ has ...
user515481
2
votes
0
answers
216
views
Confusion regarding special parahoric subgroups of the unitary group
This question is to clarify some confusion about special parahoric subgroups of a unitary group $G = \mathrm U_n(F)$ in an odd number of variables, with respect to an unramified quadratic extension $E/...
- 769
2
votes
0
answers
168
views
Galois representation absolutely irreducible after restricting to open subgroup of finite index
Let $E$ and $F$ be finite extensions of $\mathbb{Q}_p$. Let $\phi:\mathrm{Gal}(\overline{E}/E)\to GL_n(F)$ be an absolutely irreducible continuous representation. Assume that the restriction of $\phi$ ...
user158636