CAPITAL REGION ALGEBRA/NUMBER THEORY SEMINAR Speaker: Professor Cristian Lenart, Univ. at Albany Time: Wednesday, November 5, at 4:30pm Place: Harder Hall 202, Skidmore College Title: K-Theory, Representation Theory, and Affine Weyl Groups (Part II) Abstract: This is a continuation of my previous talk in the Algebra seminar at SUNY, where I gave a brief introduction to the representation theory of complex semisimple Lie groups and to the Littelmann path model. I will now focus on the geometric counterpart of the previous talk, related to the T-equivariant K-theory of a generalized flag variety G/B (where G is a complex semisimple Lie group, B a Borel subgroup, and T a maximal torus). I will discuss a Chevalley-type multiplication formula in the Grothendieck ring of coherent T-equivariant sheaves on G/B; this formula is due to H. Pittie and A. Ram, and is in terms of Littelmann paths. Then I will show that this formula implies one for Demazure characters, which are characters of the B-modules dual to the spaces of global sections of line bundles on Schubert varieties; the Weyl modules discussed in the previous talk are special cases. I will also briefly mention affine Weyl groups at the end of my talk, as a preparation for a future CRANTS talk, in which I will present a more efficient model than Littelmann paths for both K-theory of G/B and representation theory. I plan to make the talk accesible without much geometric background. Refreshments at 4:15 pm in Harder Hall 202.