Add to ORKGWe consider the system of quantum differential equations for a partial flag variety and construct a basis of solutions in the form of multidimensional hypergeometric functions, that is, we construct a Landau-Ginzburg mirror for that partial flag variety. In our construction, the solutions are labeled by elements of the $K$-theory algebra of the partial flag variety. To establish these facts we consider the equivariant quantum differential equations for a partial flag variety and introduce a compatible system of difference equations, which we call the qKZ equations. We construct a basis of solutions of the joint system of the equivariant quantum differential equations and qKZ difference equations in the form of multidimensional hypergeomet...
We use Drinfeld style generators and relations to define an algebra $\mathfrak{U}_n$ which is a "$q=...
This paper is the first in a series on graphical calculus for quantum vertex operators. We establish...
In this article, we construct a new type of degenerate q-sigmoid (DQS) polynomial for sigmoid functi...
We describe \,$q$-hypergeometric solutions of the equivariant quantum differential equations and ass...
80 pages. Typos and some mistakes corrected. Exposition improved in section 9. References updated an...
We describe q-hypergeometric solutions of the equivariant quantum differential equations and associ...
International audienceWe consider mirror symmetry (A-side vs B-side, namely singularity side) in the...
International audienceThe purpose of this article is to analyze the connection between Eynard-Oranti...
Abstract. Cherednik attached to an affine Hecke algebra module a compatible system of difference equ...
We use the double affine Hecke algebra of type GLN to construct an explicit consis-tent system of q-...
We give a systematic discussion of the relation between q-difference equations which are conditional...
We use to construct an explicit consistent system of q-difference equations, which we call the bispe...
Some of the theorems of existence of local and global solutions of quantum partial differential equa...
We investigate a system of differential equations for the beta function of massless scalar $\phi^4$ ...
The content of this paper was previously included in arXiv:1002.4839International audienceWe establi...
We use Drinfeld style generators and relations to define an algebra $\mathfrak{U}_n$ which is a "$q=...
This paper is the first in a series on graphical calculus for quantum vertex operators. We establish...
In this article, we construct a new type of degenerate q-sigmoid (DQS) polynomial for sigmoid functi...
We describe \,$q$-hypergeometric solutions of the equivariant quantum differential equations and ass...
80 pages. Typos and some mistakes corrected. Exposition improved in section 9. References updated an...
We describe q-hypergeometric solutions of the equivariant quantum differential equations and associ...
International audienceWe consider mirror symmetry (A-side vs B-side, namely singularity side) in the...
International audienceThe purpose of this article is to analyze the connection between Eynard-Oranti...
Abstract. Cherednik attached to an affine Hecke algebra module a compatible system of difference equ...
We use the double affine Hecke algebra of type GLN to construct an explicit consis-tent system of q-...
We give a systematic discussion of the relation between q-difference equations which are conditional...
We use to construct an explicit consistent system of q-difference equations, which we call the bispe...
Some of the theorems of existence of local and global solutions of quantum partial differential equa...
We investigate a system of differential equations for the beta function of massless scalar $\phi^4$ ...
The content of this paper was previously included in arXiv:1002.4839International audienceWe establi...
We use Drinfeld style generators and relations to define an algebra $\mathfrak{U}_n$ which is a "$q=...
This paper is the first in a series on graphical calculus for quantum vertex operators. We establish...
In this article, we construct a new type of degenerate q-sigmoid (DQS) polynomial for sigmoid functi...