Related papers: How to sheafify an elliptic quantum group
We define a sheafified elliptic quantum group for any symmetric Kac-Moody Lie algebra. This definition is naturally obtained from the elliptic cohomological Hall algebra of a preprojective algebra. The sheafified elliptic quantum group is…
We construct a global geometric model for complex analytic equivariant elliptic cohomology for all compact Lie groups. Cocycles are specified by functions on the space of fields of the two-dimensional sigma model with background gauge…
In this paper, we study the classical and quantum equivariant cohomology of Nakajima quiver varieties for a general quiver Q. Using a geometric R-matrix formalism, we construct a Hopf algebra Y_Q, the Yangian of Q, acting on the cohomology…
There are two intriguing statements regarding the quantum cohomology of partial flag varieties. The first one relates quantum cohomology to the affinisation of Lie algebras and the homology of the affine Grassmannian, the second one…
Quasi-elliptic cohomology is a variant of Tate K-theory. It is the orbifold K-theory of a space of constant loops. For global quotient orbifolds, it can be expressed in terms of equivariant K-theories. In this paper we show how this theory…
We construct geometric categorical Lie algebra actions on the derived category of coherent sheaves on Nakajima quiver varieties. These actions categorify Nakajima's construction of Kac-Moody algebra representations on the K-theory of quiver…
We propose a construction of some canonical bases for quantum loop algebras of Kac-Moody algebras. We consider a smooth projective curve X, a group of automorphism G of X such that X/G=P^1, and we consider some Quot schemes of G-equivariant…
We provide and study an equivariant theory of group (co)homology of a group G with coefficients in a gamma-equivariant G-module A, when a separate group "gamma" acts on G and A, generalizing the classical Eilenberg-MacLane (co)homology of…
We present a brief introduction to quantum sheaf cohomology, a generalization of quantum cohomology based on the physics of the (0,2) nonlinear sigma model.
The purpose of this paper is to present a mathematical theory of the half-twisted $(0,2)$ gauged linear sigma model and its correlation functions that agrees with and extends results from physics. The theory is associated to a smooth…
We construct certain Steinberg groups associated to extended affine Lie algebras and their root systems. Then by the integration methods of Kac and Peterson for integrable Lie algebras, we associate a group to every tame extended affine Lie…
We construct the quantum double ramification hierarchy associated with the Gromov-Witten theory of elliptic curves. We use results of Oberdieck and Pixton on the intersection numbers of the double ramification cycle, the Gromov-Witten…
In this paper, we describe a categorical action of any Kac-Moody algebra on a category of quantized coherent sheaves on Nakajima quiver varieties. By "quantized coherent sheaves," we mean a category of sheaves of modules over a deformation…
The problem of introducing a dependence of elements of quantum group on classical parameters is considered. It is suggested to interpret a homomorphism from the algebra of functions on quantum group to the algebra of sections of a sheaf of…
Using the Kontsevich's moduli space of stable maps, we define the equivariant quantum cohomology for generalized flag varieties and make a rigorous computation of quantum cohomology of flag varieties.
Quantum toroidal algebras (or double affine quantum algebras) are defined from quantum affine Kac-Moody algebras by using the Drinfeld quantum affinization process. They are quantum groups analogs of elliptic Cherednik algebras (elliptic…
We generalize a theorem of Kapranov by showing that the Hall algebra of the category of coherent sheaves on a weighted projective line (over a finite field) provides a realization of the (quantized) enveloping algebra of a certain nilpotent…
Quasi-elliptic cohomology is a variant of elliptic cohomology theories. It is the orbifold K-theory of a space of constant loops. For global quotient orbifolds, it can be expressed in terms of equivariant K-theories. Thus, the constructions…
By using twist construction, we obtain a quantum groupoid $\cald\ot_{q}\uqg$ for any simple Lie algebra $\frakg$. The underlying Hopf algebroid structure encodes all the information of the corresponding elliptic quantum group-the quasi-Hopf…
We study global primary decompositions in the category of sheaves on a scheme which are equivariant under the action of an algebraic group. We show that equivariant primary decompositions exist if the group is connected. As main application…