On Bessel distributions for quasi-split groups (Q2719036)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On Bessel distributions for quasi-split groups |
scientific article; zbMATH DE number 1597927
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Bessel distributions for quasi-split groups |
scientific article; zbMATH DE number 1597927 |
Statements
On Bessel distributions for quasi-split groups (English)
0 references
14 May 2001
0 references
Bessel function
0 references
local field
0 references
quasi-split reductive group
0 references
Bessel distribution
0 references
Let \(F\) be a local field and let \(G\) be a quasi-split reductive group defined over \(F\). Let \(\pi\) be a generic representation of \(G(F)\). The author then shows that the Bessel distribution in the so-called Bessel model of \(\pi\) is in fact a function on the open Bruhat cell. In fact the function (Bessel function) is real analytic in the archimedean case and locally constant in the non-archimedean case. The proof involves a close analysis of the distribution and its relation to the compact open subgroups of \(G(F)\).
0 references
