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>