All Questions
10 questions
5
votes
1
answer
230
views
Explicit Jacquet-Langlands correspondence for real reductive groups
Let $G$ be a connected reductive group over $\mathbb R$. Let $G'$ over $\mathbb R$ be an inner form of $G$ with ${}^LG={}^LG'$. By local Langlands correspondence over $\mathbb R$, if a $L$-packet of $...
- 6,622
11
votes
0
answers
283
views
Why are there so few irreducible admissible representations of $\text{GL}(n,\mathbb{R})$ (up to infinitesimal equivalence)?
Studying Langlands's classification of irreducible admissible representations, I have been rather stunned by the following:
Theorem
Up to infinitesimal equivalence, all irreducible admissible ...
- 511
6
votes
1
answer
551
views
Two definitions of automorphic forms on Lie groups
My question is the about the equivalence of two definitions of automorphic forms on a semisimple Lie group.
The most common definition of automorphic forms on a semisimple Lie group $G$ with respect ...
- 391
6
votes
1
answer
764
views
What is a map for the representation theory of reductive groups?
I have finished learning about linear algebraic groups (minus their representation theory) and the associated algebraic structures (root data, root systems, etc.), and will next attempt to summarize ...
- 2,071
12
votes
1
answer
418
views
When does a locally symmetric space have no odd degree Betti numbers?
Let $G$ be a semisimple real lie group, $K$ be a maximal compact subgroup of $G$, $\Gamma$ be a torsion-free cocompact discrete subgroup. The Betti number the locally symmetric space $X_{\Gamma}:=\...
- 6,622
3
votes
0
answers
188
views
Non-vanishing of left- vs. right-averages over lattices in $SL(2,\mathbb{R})$
I asked the same question on MSE one week ago, but it has not received any answers.
Background. Let $G=SL(2,\mathbb{R})$, let $K=SO(2)$, and let $\Gamma$ be a lattice in $G$, e.g. $SL(2,\mathbb{Z})$...
- 229
6
votes
0
answers
1k
views
Definition of Admissible Representation
Let $G$ be a connected, reductive group over a number field $k$. Let $v$ be a place of $k$.
If $v$ is finite, an admissible representation of $G(k_v)$ is defined to be an abstract representation of $...
- 6,180
8
votes
1
answer
1k
views
Multiplicity one theorem
I am reading Dorian Goldfeld's book Automorphic forms and L functions for the groups GL(n,R) (http://www.cambridge.org/us/academic/subjects/mathematics/number-theory/automorphic-forms-and-l-functions-...
1
vote
0
answers
110
views
On continuous part of the L^2 spectrum
Suppose $G$ is a real reductive Lie group and $\Gamma$ is a lattice in $G$ (of finite co-volume). I am reading Langlands's paper " On the functional equation satisfied by the Eisenstein series". I ...
- 61
7
votes
1
answer
561
views
How does the right regular of GL(n, R) and GL(n,Qp) decompose?
The question is contained in the title. I would guess that this question is already answered in the literature.
Given the reductive group $GL(n)$ over a complete local field, how does the right ...
- 11.2k