A combinatorial model for representations of Kac-Moody algebras

Infinite-Dimensional Algebra Seminar, MIT

May 06, 2005

Alexander Postnikov
                                                                                
Abstract:
                                                                                
     We  present a  combinatorial  model for  characters of  irreducible
representations of Kac-Moody  algebras.  The model is  based on counting
saturated chains  in the Weyl  group and interlaced sequences  of roots.
This  model  is  a  combinatorial counterpart  of  the  Littelmann  path
model.  We describe a crystal graph structure and deduce a combinatorial
Littlewood-Richardson   rule   for   decomposing  tensor   products   of
irreducible representations and  a branching rule.  In  the finite case,
the model  has a geometric  interpretation in  terms of alcoves  for the
associated Langland's dual affine Weyl group.  We use this model to give
a  Chevalley-type formula  for the  equivariant K-theory  of generalized
flag varieties.  This is joint work with C. Lenart.