Abstract

We 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 coefficients. We state some open problems related with our quadratic algebras. (work partly joint with S Fomin)