Affine nil-Hecke algebras and braided differential structure on affine Weyl groups
Anatol N. Kirillov, Toshiaki Maeno
TL;DR
This paper constructs a model of the affine nil-Hecke algebra within a Nichols-Woronowicz algebra framework and explores its implications for the homology of affine Grassmannians and quantum cohomology.
Contribution
It introduces a novel algebraic model linking affine nil-Hecke algebras with braided differential calculus and affine Weyl groups.
Findings
Established a subalgebra model of affine nil-Hecke algebra in Nichols-Woronowicz algebra
Connected the Peterson isomorphism to braided differential calculus
Provided new insights into the structure of affine Grassmannian homology
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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Combinatorial Mathematics