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

Anatol N. Kirillov | Zendy; Toshiaki Maeno | Zendy

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

Author(s) -

Anatol N. Kirillov,

Toshiaki Maeno

Publication year - 2012

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/67

Subject(s) - mathematics , pure mathematics , affine transformation , isomorphism (crystallography) , cohomology ring , subalgebra , cohomology , affine representation , affine group , algebra over a field , quantum affine algebra , weyl group , affine variety , differential (mechanical device) , cellular algebra , algebra representation , affine lie algebra , equivariant cohomology , current algebra , engineering , aerospace engineering , chemistry , crystal structure , crystallography

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.

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