AbstractWe introduce certain class of quadratic algebras together with commutative subalgebras generated by additive and multiplicative Dunkl elements correspondingly. We identify these subalgebras with cohomology and K-theories of type A flag varieties. We show that value of Schubert polynomials on additive Dunkl elements is a generating function for the corresponding Littlewood-Richardson coe...
Abstract: We will report on an ongoing project with R. Bezrukavnikov and L. Rider which aims at constructing an equivalence of categories lifting to the categorical level the comparison between the two natural geometric realizations of the affine Hecke algebra of a reductive group: one in terms of constructible sheaves on the associated affine flag variety, and one in terms of coherent sheaves ...