We construct a model of the affine nil-Hecke algebra as a subalgebra of theNichols-Woronowicz algebra associated to a Yetter-Drinfeld module over theaffine Weyl group. We also discuss the Peterson isomorphism between thehomology of the affine Grassmannian and the small quantum cohomology ring ofthe flag variety in terms of the braided differential calculus.
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