CAPITAL REGION ALGEBRA/NUMBER THEORY SEMINAR 


Speaker:       Professor Cristian Lenart, Univ. at Albany 

Time:          Wednesday, November 19, at 4:30pm 

Place:         Earth Sciences Bldg. 152A, Univ. at Albany 

Title:         A New Model for the K-Theory of G/B and 
               the Representation Theory of G
 
Abstract:

I will present a simple model for characters of irreducible
representations of semi-simple Lie groups and, more generally, for
Demazure characters. This model simplifies the Littelmann path model, as
well as a more recent related construction due to Gaussent and
Littelmann (called LS-galleries). Based on the new model, I will also
present an explicit combinatorial Chevalley-type multiplication formula
for the equivariant K-theory of generalized flag varieties G/B.  The
construction is given in terms of alcove paths, which correspond to
decompositions of affine Weyl group elements, as well as saturated
chains in the Bruhat order on the usual Weyl group.  A key ingredient is
a certain R-matrix that satisfies the Yang-Baxter equation. This is a
joint work with Alexander Postnikov from MIT. The background material,
which was presented in two previous talks, will be reviewed at the
beginning of the current talk. I will also present some examples, and
will devote a future talk to additional concrete computations based on
the new model.


Refreshments at 4:15 pm in ES 152.