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>