Related papers: Quantized multiplicative quiver varieties
We construct the action of the quantum double of $\uq$ on the standard Podle\'s sphere and interpret it as the quantum projective formula generalizing to the q-deformed setting the action of the Lorentz group of global conformal…
By using the equivariant theory of group actions, we give a geometric model for the category of finite dimensional representations over a type $\mathbb{D}$ quiver $Q_{D}$ with $n$ vertices and directional symmetry. Furthermore, we introduce…
For a finite dimensional semisimple Lie algebra ${\frak{g}}$ and a root $q$ of unity in a field $k,$ we associate to these data a double quiver $\bar{\cal{Q}}.$ It is shown that a restricted version of the quantized enveloping algebras…
Consider the generalized flag manifold $G/B$ and the corresponding affine flag manifold $\mathcal{Fl}_G$. In this paper we use curve neighborhoods for Schubert varieties in $\mathcal{Fl}_G$ to construct certain affine Gromov-Witten…
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…
Inside the double affine Hecke algebra of type $GL_n$, which depends on two parameters $q$ and $\tau$, we define a subalgebra $\mathbb{H}^{\mathfrak{gl}_n}$ that may be thought of as a $q$-analogue of the degree zero part of the…
We introduce an analogue of the $q$-Schur algebra associated to Coxeter systems of type $\hat A_{n-1}$. We give two constructions of this algebra. The first construction realizes the algebra as a certain endomorphism algebra arising from an…
We define and study cyclotomic quotients of affine Hecke algebras of type D. We establish an isomorphism between (direct sums of blocks of) these cyclotomic quotients and a generalisation of cyclotomic quiver Hecke algebras which are a…
Let $U_q(\hat{\cal G})$ be a quantized affine Lie algebra. It is proven that the universal R-matrix $R$ of $U_q(\hat{\cal G})$ satisfies the celebrated conjugation relation $R^\dagger=TR$ with $T$ the usual twist map. As applications, braid…
We present a simple unified formula expressing the denominators of the normalized R-matrices between the fundamental modules over the quantum loop algebras of type ADE. It has an interpretation in terms of representations of the Dynkin…
We consider an infinite quiver $Q(\mathfrak{g})$ and a family of periodic quivers $Q_m(\mathfrak{g})$ for a finite dimensional simple Lie algebra $\mathfrak{g}$ and $m \in \mathbb{Z}_{>1}$. The quiver $Q(\mathfrak{g})$ is essentially same…
We first provide an explicit combinatorial description of the Auslander-Reiten quiver $\Gamma^Q$ of finite type $D$. Then we can investigate the categories of finite dimensional representations over the quantum affine algebra…
Given a real number $q$ such that $0<q<1$, the natural setting for the mathematics of a $q$-oscillator is an infinite-dimensional, separable Hilbert space that is said to provide an interpolation between the Bargmann-Segal space of…
In this paper we study general quantum affinizations $\U_q(\hat{\Glie})$ of symmetrizable quantum Kac-Moody algebras and we develop their representation theory. We prove a triangular decomposition and we give a classication of (type 1)…
We compute the factorisation homology of the four-punctured sphere and punctured torus over the quantum group $\mathcal{U}_q(\mathfrak{sl}_2)$ explicitly as categories of equivariant modules using the framework of `Integrating Quantum…
Let $X$ be a variety with an action by an algebraic group $G$. In this paper we discuss various properties of $G$-equivariant $D$-modules on $X$, such as the decompositions of their global sections as representations of $G$ (when $G$ is…
Given a quiver, a fixed dimension vector, and a positive integer n, we construct a functor from the category of D-modules on the space of representations of the quiver to the category of modules over a corresponding Gan-Ginzburg algebra of…
An embedding method to get $q$-deformations for the non--semisimple algebras generating the motion groups of $N$--dimensional flat spaces is presented. This method gives a global and simultaneous scheme of $q$-deformation for all $iso(p,q)$…
Commutative sets of Jucys-Murphyelements for affine braid groups of $A^{(1)},B^{(1)},C^{(1)},D^{(1)}$ types were defined. Construction of $R$-matrix representations of the affine braid group of type $C^{(1)}$ and its distinguish commutative…
The paper is constructed in two parts.In the first part we introduce the concept of the algebra of Q-meromorphic functions on the quantum plane.The A (q)-algebra of Q-analytic functions considered in[6]is seen as a proper subalgebra. In the…