| 発表言語 |
日本語
|
| 開催日 |
2009年06月03日 16時30分
|
| 終了日 |
2009年06月03日 17時30分
|
| 開催場所 | 京都大学数理解析研究所202号室 |
| セミナー名 | 談話会 |
| タイトル |
Shintani's formula for Whittaker functions and its q,t-generalization |
| 分野 |
代数
幾何
解析
その他
|
| 講演者名 | Ivan Cherednik |
| 講演者所属 | The University of North Carolina at Chapel Hill |
| 概要 | We will begin with the Shintani-Casselman-Shalika
formula for the p-adic unramified Whittaker function.
Surprisingly, it does not depend on p (in a suitable
normalization), which has no clear explanation in the
p-adic theory. To understand this phenomenon and other
features of the p-adic Whittaker function, one needs
to extend it to the q-Whittaker function, which, among
other its properties, interpolates between the p-adic
and real Whittaker functions. Moreover, another step
is needed, the q,t-theory. At this level, the Shintani
formula becomes the specialization theorem for the
difference spherical function, generalizing the basic
hypergeometric function and the Macdonald polynomials.
The q-Whittaker functions attract attention now because
of their connection with the affine flag varieties and,
possibly, the quantum Langlands program. The Shintani
formula will be introduced from scratch, including an
outline of its justification.
|
|