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8 votes
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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 …
Jianrong Li's user avatar
  • 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:/ …
Jianrong Li's user avatar
  • 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 …
Jianrong Li's user avatar
  • 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 …
Jianrong Li's user avatar
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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) …
Jianrong Li's user avatar
  • 6,201