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>