JournalsprimsVol. 48, No. 1pp. 215–228

Affine Nil-Hecke Algebras and Braided Differential Structure on Affine Weyl Groups

  • Anatol N. Kirillov

    Kyoto University, Japan
  • Toshiaki Maeno

    Kyoto University, Japan
Affine Nil-Hecke Algebras and Braided Differential Structure on Affine Weyl Groups cover
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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.

Cite this article

Anatol N. Kirillov, Toshiaki Maeno, Affine Nil-Hecke Algebras and Braided Differential Structure on Affine Weyl Groups. Publ. Res. Inst. Math. Sci. 48 (2012), no. 1, pp. 215–228

DOI 10.2977/PRIMS/67