Trigonometric Grassmannian and a difference W-algebra

Analysis Seminar
Wednesday, September 30, 2009 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 269
Plamen Illiev – Georgia Tech
Brett Wick
The trigonometric Grassmannian parametrizes specific solutions of the KP hierarchy which correspond to rank one solutions of a differential-difference bispectral problem. It can be considered as a completion of the phase spaces of the trigonometric Calogero-Moser particle system or the rational Ruijsenaars-Schneider system. I will describe the characterization of this Grassmannian in terms of representation theory of a suitable difference W-algebra. Based on joint work with L. Haine and E. Horozov.