The Weizmann Institute of Science Faculty of Mathematics and Computer Science Algebraic Geometry and Representation Theory Seminar Seminar Room, Room 261, Ziskind Building on Thursday, January 10, 2013 at 17:00 Anton Khoroshkin Stony Brook University will speak on BGG repciprocity for current algebras Abstract: I will consider the category of modules over current Lie algebra $g\otimes C[t]$ which are integrable with respect to the semisimple Lie subalgebra $g$. The purpose of the talk is to show that this category is similar to the usual category $O$. In particular, the irreducible modules are the same and are numbered by dominant weights. However, Verma modules are replaced by so called Weyl modules, moreover, projective covers of irreducibles admits filtration by the latter analogs of Verma modules and there exists a duality theorem for multiplicities that generalises the classical BGG duality theorem. Duality theorem may be used in order to show that the characters of Weyl modules are given by MacDonald polynomials for $t=0$. The talk is partially based on the joint work <http://arxiv.org/abs/1207.2446> --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Yaeli Malka <yaeli.malka@weizmann.ac.il>