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, May 16, 2012
                                    at 11:40
 
                         Note the unusual day and time
 
                                 Ivan Cherednik
 
                                 will speak on
 
                           Global spherical functions

Abstract:
The affine Demazure characters are one of the main objects in the Kac-Moody
representation theory. In the level one case, the corresponding quadratic-type
generating functions were proven several years ago to be (very remarkable)
solutions of the q-Toda eigenvalue problem. It was done only for dominant
(W-invariant) Demazure characters; the general case is in progress (for
level=1).

Importantly, the simplest way of arriving at this theorem/theory is via its
q,t-deformation followed by the limit $t-->0$. The corresponding generating
functions were called global spherical functions due to their analyticity
anywhere; they solve the Macdonald-Ruijsenaars eigenvalue problem and go
through the Macdonald polynomials for dominant weights (through the Demazure
characters in the limit).
 
---------------------------------------------------------
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Yaeli Malka   <yaeli.malka@weizmann.ac.il>