25 citations · 86 across the 22 of their papers we have counts for
10 papers · 1 filter
A presentation of the torus-equivariant quantum -theory ring of flag manifolds of type , Part II: quantum double Grothendieck polynomials
Toshiaki Maeno, Satoshi Naito, Daisuke Sagaki
In our previous paper, we gave a presentation of the torus-equivariant quantum -theory ring of the (full) flag manifold of type as a quotie…
A presentation of the torus-equivariant quantum -theory ring of flag manifolds of type , Part I: the defining ideal
Toshiaki Maeno, Satoshi Naito, Daisuke Sagaki
We give a presentation of the torus-equivariant quantum -theory ring of flag manifolds of type , as a quotient of a polynomial ring by an explicit ideal. This is the torus-eq…
Affine nil-Hecke algebras and braided differential structure on affine Weyl groups
Anatol N. Kirillov, Toshiaki Maeno
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 di…
Extended quadratic algebra and a model of the equivariant cohomology ring of flag varieties
Anatol N. Kirillov, Toshiaki Maeno
For the root system of type we introduce and study a certain extension of the quadratic algebra invented by S. Fomin and the first author, to construct a model for the equivari…
Braided differential structure on Weyl groups, quadratic algebras and elliptic functions
Anatol N. Kirillov, Toshiaki Maeno
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…
Nichols-Woronowicz model of coinvariant algebra of complex reflection groups
Anatol N. Kirillov, Toshiaki Maeno
We give a model of the coinvariant algebra of the complex reflection groups as a subalgebra of a braided Hopf algebra called Nichols-Woronowicz algebra.
Alcove path and Nichols-Woronowicz model of the equivariant -theory of generalized flag varieties
Cristian Lenart, Toshiaki Maeno
Fomin and Kirillov initiated a line of research into the realization of the cohomology and -theory of generalized flag varieties as commutative subalgebras of certain nonc…
Alcove path and Nichols-Woronowicz model of -theory on flag varieties
Toshiaki Maeno
This paper has been withdrawn.
A note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groups
Anatol. N. Kirillov, Toshiaki Maeno
We give a description of the (small) quantum cohomology ring of the flag variety as a certain commutative subalgebra in the tensor product of the Nichols algebras. Our main result…
Exterior differential algebras and flat connections on Weyl groups
Anatol N. Kirillov, Toshiaki Maeno
We study some aspects of noncommutative differential geometry on a finite Weyl group in the sense of S. Woronowicz, K. Bresser {\it et al.}, and S. Majid. For any finite Weyl group…