CAPITAL REGION ALGEBRA/NUMBER THEORY SEMINAR 


Speaker:       Cristian Lenart, Univ. at Albany  

Time:          Wednesday, November 17, at 4:30pm       

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

Title:         A New Model in the Representation Theory 
               of Kac-Moody Algebras


Abstract:

We have recently defined a new combinatorial model for the 
Chevalley-type multiplication formula in the equivariant K-theory of 
generalized flag varieties  G/B  associated with simple complex Lie 
groups  G. In the present paper, we develop this model purely within 
the representation theory of  G. In doing so, we extend our model to 
the representation theory of symmetrizable Kac-Moody algebras. We use 
this model to express the characters of the irreducible integrable 
highest weight modules and to describe the corresponding crystal graph. 
We also present a Littlewood-Richardson rule for decomposing tensor 
products of the mentioned representations. The new model is 
combinatorial, being based on certain chains of roots. This is a joint 
work with Alex Postnikov.


Refreshments at 4:15 pm in ES 152.