The Weizmann Institute of Science Faculty of Mathematics and Computer Science Algebraic Geometry and Representation Theory Seminar Seminar Room, Room 261, Ziskind Building on Tuesday, October 25, 2011 11:00 - 12:30 (Note the unusual day) Dmitry Gourevitch will speak on Degenerate Whittaker functionals on representations of real reductive groups Abstract: It was proven by Nakayama that for modules over commutative algebras, the support can be measured by existence of functionals equivariant with respect to different characters of the algebra. For smooth representations of reductive groups over local fields, one is interested in functionals equivariant with respect to characters of the nilradical of Borel subgroups. Functionals equivariant with respect to non-degenerate characters are called Whittaker functionals. It was shown by Rodier in the p-adic case and Kostant in the archimedean case that an irreducible representation has (non-zero) Whittaker functionals if and only if it has maximal wavefront set / associated variety. In the p-adic case, the correspondence between existence of other equivariant functionals and the wavefront set was found by Moeglen and Waldspurger, and in the real case there are partial results by Matumoto, establishing in some cases a connection between the associated variety and existence of functionals equivariant w.r.t. non-degenerate characters of nilradicals of (bigger) parabolic subgroups. In our joint work with S. Sahi, we take a different path and establish a a precise connection between the associated variety of a representation and the existence of functionals equivariant w.r.t. (degenerate) characters of nilradicals of the Borel subgroup. Remark. This is a "preseason" meeting in an unusual day. The next talk will be on the first Monday of the semester, Nov 7, by Alexander Rahm. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Yaeli Malka <yaeli.malka@weizmann.ac.il>