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Results tagged with automorphic-forms
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user 11877
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.
8
votes
1
answer
612
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Bernstein–Zelevinsky classification for classical groups
Bernstein and Zelevinsky classifies the irreducible complex smooth representations of a general linear group over a local field in terms of cuspidal representations. The irreducible modules are parame …
- 6,201
8
votes
2
answers
954
views
Relation between representations of p-adic groups and affine Hecke algebras
Let $R_n$ be the category of complex-valued smooth finite-length representations of the group $GL_n(F)$, where $F$ is a local field.
By the result of Borel, the subcategory of $R_n$ consisting of repr …
- 6,201
4
votes
0
answers
390
views
Why Whittaker functions are useful?
Whittaker functions appears in Langlands program. Recently, it is shown that some Whittaker functions can be obtained by integrating a function related to decoration over a geometric crystal in http:/ …
- 6,201
3
votes
1
answer
484
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What is the current status of representations of $GL_n(F)$ (and other algebraic groups)?
What is the current status of representations of $GL_n(F)$ (and other algebraic groups)?
When $F$ is a local field, the representations of $GL_n(F)$ are classified by Bernstein and Zelevinsky in ter …
- 6,201
3
votes
1
answer
364
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References about identities of Gauss sum
I am reading the paper. In the end of page 10, there are the following identities of Gauss sum.
\begin{align}
& h(b) h(a+b) = q^b h(b) h(a), \\
& h(b) g(a+b) = q^b h(b) g(a), \\
& g(a+b) h(a) h(b) = h …
- 6,201
2
votes
1
answer
399
views
Two questions about Whittaker functions
I am watching the video: Modeling p-adic Whittaker functions, Part I. I have two questions about Whittaker functions in the video.
From 33:00 to 37:00, it is said that after changing of variables, w …
- 6,201
2
votes
0
answers
245
views
Reference request: proofs of the theorems in the paper "On the representation of the group G...
In the paper On the representation of the group $GL(n, K)$ where $K$ is a local field by Gelfand and Kazhdan, it is said that the proofs of the theorems in the paper are published in some other papers …
- 6,201
2
votes
1
answer
422
views
A computation about Whittaker functions and Eisenstein series
I have some questions about the computation of Eisenstein series and Whittaker functions in the book. The question is on page 29, Theorem 4.3.
My questions are in the following.
(1) I think that …
- 6,201
1
vote
Two questions about Whittaker functions
In the case of $SL_2$, we have
$$
U = \left\{ \left(\begin{matrix} 1 & x \\ 0 & 1 \end{matrix}\right) : x \in F \right\}
$$
and
\begin{align}
& \int_U f^0\left( w_0 u t_{\lambda} \right) \psi^{-1}(u) …
- 6,201
1
vote
0
answers
152
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What are the differences between p-adic Whittaker functions and archimedean Whittaker functi... [closed]
What are the differences between p-adic Whittaker functions and archimedean Whittaker functions? Are there some references about the differences? Thank you very much.
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