Séminaire Groupes Réductifs et Formes Automorphes
Alexis Bouthier, Francesco Lemma
Email des responsables :
Dmitry Gourevitch - Weizmann Institute of Science,
Generalized and degenerate Whittaker models
10:30 à 12:00
The Whittaker model is a very useful tool in the representation theory of reductive groups and in automorphic forms. However, it is known that only the largest representations have Whittaker models. In order to overcome this problem, for other representations various kinds of degenerate or generalized Whittaker models are considered since the 80s.
Over non-archimedean fields, Moeglen and Waldspurger characterized the existence and multiplicities of these models in terms of the wave-front set. For $\mathrm
(n, F)$ they can be also described in terms of the Bernstein-Zelevinsky derivatives. Over the Archimedean fields, only partial results are known in this direction. I want to talk about these partial results, including my recent works with Siddhartha Sahi (and sometimes others) on degenerate Whittaker models, Archimedean Bernstein-Zelevinsky derivatives and the connection between them. Some of these results are new also over $p$-adic fields. Some of the results also have adelic analogues.