Affine Nil-Hecke algebras and braided differential structure on affine weyl groups

Abstract

We construct a model of the affine nil-Hecke algebra as a subalgebra of the Nichols- Woronowicz algebra associated to a Yetter- Drinfeld module over the affine Weyl group. We also discuss the Peterson isomorphism between the homology of the affine Grassmannian and the small quantum cohomology ring of the flag variety in terms of the braided differential calculus. © 2012 Research Institute for Mathematical Sciences, Kyoto University.