Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with automorphic-forms
Search options questions only
not deleted
user 29422
An automorphic form is a well-behaved function from a topological group $G$ to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup $\Gamma \subset G$ of the topological group. Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups.
7
votes
1
answer
276
views
Restriction of product of automorphic forms
Let $W \subset V$ be quadratic spaces over a number field $F$.
Let $G_n=SO(V)$ and $G_m=SO(W)$ and we consider $G_m$ as a subgoup of $G_n$ via a diagonal embedding.
Let $f$ be an automorphic form of …
- 1,759
6
votes
1
answer
364
views
Local component of cuspidal automorphic representation
Let $F$ be a number field and $\mathbb{A}$ its adele ring. $G$ be a classical group and $
\pi$ be a unitary cuspidal automorphic representation of $G(\mathbb{A})$.
Then I am wondering whether there is …
- 1,759
5
votes
1
answer
399
views
Is the restriction of a representation semisimple?
Let $F$ be local field of characteristic zero and $\pi$ be a irreducible admissible representation of $GL_n(F)$.
Let us consider its restriction to $GL_{n-1}(F)$. Then I want to know whether $\pi|_{G …
- 1,759
5
votes
1
answer
473
views
Explicit formula of base change for GL(n)
Let $E/F$ be a quadratic extension of number fields and $v$ is a place of $F$.
Let $\chi_1,\chi_2$ be the unramified characters of $F_v^{\times}$.
If $B(\chi_1,\chi_2)$ is the unramified principal s …
- 1,759
5
votes
2
answers
719
views
What condition makes unitary reductive group unramified?
I am a little bit confused with the definition of an unramified unitary group.
Let $F$ be a local field of characteristic zero whose residue field is finite field of characteristic $p$.
Then for a c …
- 1,759
4
votes
1
answer
249
views
Projection onto locally constant function
I am asking a question which looks very elementary to experts.
Let $F$ be a number field and $\mathbb{A}_F$ its adele ring. Let $\omega$ be a unitary central character of $GL_2(\mathbb{A}_F)$,
$X_{ …
- 1,759
4
votes
0
answers
122
views
$L^2$-spectrum versus automorphic discrete spectrum
Let $G$ be a classical group defined over a number field $F$.
In his monumental book, (https://www.ams.org/books/coll/061/coll061-endmatter.pdf) Arthur described a spectral decomposition of $L_{disc}^ …
- 1,759
3
votes
0
answers
245
views
Some basic question on the parabolic induction
I would like to ask some basic question about parabolic induction.
Let $F$ be a local field and $G=GL_n(F)$ and $P=MN$ its parabolic subgroup whose Levis subgroup $M=GL_{n_1}(F) \times GL_{n_2}(F)$ w …
- 1,759
3
votes
0
answers
127
views
Is constant map from automorphic form surjective?
Let $G$ be a connected reductive group over $\mathbb{Q}$ and $P=NM$ be a standard parabolic subgroup of $G$ and and $K$ a 'good' maximal compact subgroup of $G$. (For precise definitions of these term …
- 1,759
3
votes
0
answers
151
views
Question on the proper sub-representation of induced representation
$\DeclareMathOperator\Ind{Ind}$Let $G$ be a reductive group over a $p$-adic local field $F$, and $P=MN$ a parabolic subgroup.
Let $\sigma$ be an irreducible representation of $M(F)$ and consider its …
- 1,759
3
votes
0
answers
134
views
Iwasawa decomposition on unitary group of anisotropic kernel
Let $E/F$ be a quadratic extension of number fields. If $V$ is a hermitian space over $E$, let $V=X+V_0+Y$ be its Witt decomposition, where $X,Y$ are maximal totally isotropic subspaces and $V_0$ is a …
- 1,759
3
votes
1
answer
363
views
Local component of global irreducible representation of GL_2(A_F)
In studying automourphic representation, I want to know whether my understanding is on the right way.
Let $\pi$ be a irreducible cuspidal representation of $GL_2(A_F)$.
Then $\pi_v$, the local comp …
- 1,759
3
votes
1
answer
258
views
Is there a definition of supercupidal parameter in the Local Langland correspondence?
By the recent works of Mok, and Kaletha, Shin, White, James, I know that there is a notion of tempered $L$-parameter, square integrable $L$-parameter and generic $L$-parameter of unitary groups.
Howe …
- 1,759
3
votes
0
answers
87
views
Theta lifting over function fields
Let $F$ be a number field and $\mathbb{A}$ its adele ring.
For a dual reductive pair $G$ and $H$, let $\pi$ be a cuspidal irreducible representation of $G(\mathbb{A})$. Let $\Theta(\pi)$ be the global …
- 1,759
3
votes
1
answer
559
views
The effect of base change on the L-function of GL(2)?
Let $F$ be a local field (whose residue field is $q$) and $E$ its quadratic extension. Let $\pi$ be a irreducible principal series representation $\pi(\chi_1, \chi_2)$ of $GL_F(2)$ especially where $\ …
- 1,759