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>