The  Weizmann  Institute  of  Science
                  Faculty of Mathematics and Computer Science
 
              Algebraic Geometry and Representation Theory Seminar
 
                    Seminar Room, Room 261, Ziskind Building
                        on Wednesday, February 23, 2011
                                 11:00 - 12:30
 
                                 Note unusual day 
 
                               Dmitry Gourevitch
 
                                 will speak on
 
                 On associated variety, Whittaker functionals,
              derivatives and rank for representations of GL(n,R)
 
Abstract:
There are several ways of measuring size of representations of reductive
groups. One of them is to attach to a representation a certain subvariety of
the nilpotent cone of the group. Another way is to ask whether the
representation possesses functionals equivariant with respect to some
subgroups, in particular the nilradical of the minimal parabolic. Such
functionals are called Whittaker functionals. I will discuss those notions and
report a recent result of ours that connects those notions in the case
$G=GL(n,R)$. Analogous results hold also over the fields of complex and p-adic
numbers.
 
For unitary representations we also compute the associated variety of the
highest derivative of a representation. Based on our results we suggest a new
notion of rank of a representation, which extends Howe's notion of rank.
 
This is work in progress, joint with Siddhartha Sahi.
 
---------------------------------------------------------
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Diana Mandelik   <diana.mandelik@weizmann.ac.il>