A note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groups

Braided differential structure on Weyl groups, quadratic algebras and elliptic functions

We discuss a class of generalized divided difference operators which give rise to a representation of Nichols-Woronowicz algebras associated to Weyl groups. For the root system of type A, we also study the condition for the deformations of the Fomin-Kirillov quadratic algebra, which is a quadratic lift of the Nichols-Woronowicz algebra, to admit a representation given by generalized divided dif...

Affine nil-Hecke algebras and braided differential structure on affine Weyl groups

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.

φ-factorable operators and Weyl-Heisenberg frames on LCA groups

On Pointed Hopf Algebras with Classical Weyl Groups

Many cases of infinite dimensional Nichols algebras of irreducible YetterDrinfeld modules over classical Weyl groups are found. It is proved that except a few cases Nichols algebras of reducible Yetter-Drinfeld modules over classical Weyl groups are infinite dimensional. Some finite dimensional Nichols algebras of Yetter-Drinfeld modules over classical Weyl groups are given.

Combinatorial integers (m, nj) and Schubert calculus in the integral cohomology ring of infinite smooth flag manifolds

Kumar described the Schubert classes which are the dual to the closures of the Bruhat cells in the flag varieties of the Kac-Moody groups associated to the infinite dimensional KacMoody algebras [17]. These classes are indexed by affine Weyl groups and can be chosen as elements of integral cohomologies of the homogeneous space L̂polGC/B̂ for any compact simply connected semisimple Lie groupG. Lat...