Affine Weyl groups in K-theory and representation theory

Details Affine Weyl groups in K-theory and representation theory Affine Weyl groups in K-theory and representation theory

2003-09-12

arxiv.org/abs/math/0309207v3

Mathematics

Representation Theory

v2: Major revision: several new sections and an appendix added, references added, exposition improved. New material includes:

Scientific paper

We give an explicit combinatorial Chevalley-type formula for the equivariant K-theory of generalized flag varieties G/P which is a direct generalization of the classical Chevalley formula. Our formula implies a simple combinatorial model for the characters of the irreducible representations of G and, more generally, for the Demazure characters. This model can be viewed as a discrete counterpart of the Littelmann path model, and has several advantages. Our construction is given in terms of a certain R-matrix, that is, a collection of operators satisfying the Yang-Baxter equation. It reduces to combinatorics of decompositions in the affine Weyl group and enumeration of saturated chains in the Bruhat order on the (nonaffine) Weyl group. Our model easily implies several symmetries of the coefficients in the Chevalley-type formula. We also derive a simple formula for multiplying an arbitrary Schubert class by a divisor class, as well as a dual Chevalley-type formula. The paper contains other applications and examples.

Affiliated with

Also associated with

No associations

Rating

Affine Weyl groups in K-theory and representation theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Affine Weyl groups in K-theory and representation theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Affine Weyl groups in K-theory and representation theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-230622