Related papers: Combinatorial Fock spaces and quantum symmetric pa…
In this paper we express certain multiplicities in modular representation-theoretic categories of type A in terms of affine p-Kazhdan-Lusztig polynomials. The representation-theoretic categories we deal with include the categories of…
We study deformations of the harmonic oscillator algebra known as polynomial Heisenberg algebras (PHAs), and establish a connection between them and extended affine Weyl groups of type $A^{(1)}_m$, where $m$ is the degree of the PHA. To…
Let $J$ be a set of pairs consisting of good modules over an affine quantum algebra and invertible elements. The distribution of poles of the normalized R-matrices yields Khovanov-Lauda-Rouquier algebras $R^J$. We define a functor $F$ from…
For any module over the affine Weyl group we construct a representation of the associated trigonometric Cherednik algebra $A(k)$ at critical level in terms of Dunkl type operators. Under this representation the center of $A(k)$ produces…
We compute the center and Azumaya locus in the simplest non-abelian examples of quantized multiplicative quiver varieties at a root of unity: quantum Weyl algebras of rank $N$, and quantum differential operators on the quantum group…
We study the behaviors of quantum groups under an edge contraction. We show that there exists an explicit embedding induced by an edge contraction operation. We further conjecture that this explicit embedding is a section of an explicit…
For every smooth projective variety, we construct an action of the Heisenberg algebra on the direct sum of the Grothendieck groups of all the symmetric quotient stacks which contains the Fock space as a subrepresentation. The action is…
We prove that the Grothendieck rings of category $\mathcal{C}^{(t)}_Q$ over quantum affine algebras $U_q'(\g^{(t)})$ $(t=1,2)$ associated to each Dynkin quiver $Q$ of finite type $A_{2n-1}$ (resp. $D_{n+1}$) is isomorphic to one of category…
We establish an algebra-isomorphism between the complexified Grothendieck ring F of certain bimodule categories over a modular tensor category and the endomorphism algebra of appropriate morphism spaces of those bimodule categories. This…
The standard modules for an affine Lie algebra $\ga$ have natural subquotients called parafermionic spaces -- the underlying spaces for the so-called parafermionic conformal field theories associated with $\ga.$ We study the case $\ga =…
We study the space of biinvariants and zonal spherical functions associated to quantum symmetric pairs in the maximally split case. Under the obvious restriction map, the space of biinvariants is proved isomorphic to the Weyl group…
In this short note, we show that the Ginzburg-Vasserot map between the quantum affine algebra of type A_(n-1) and the equivariant K-theory group of the Steinberg Variety (of n-step flags in C^d) restricts and remains surjective at the level…
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 study the relation between quantum affine algebras of type A and Grassmannian cluster algebras. Hernandez and Leclerc described an isomorphism from the Grothendieck ring of a certain subcategory $\mathcal{C}_{\ell}$ of…
Given a Hopf algebra $A$ graded by a discrete group together with an action of the same group preserving the grading, we define a new Hopf algebra, which we call the graded twisting of $A$. If the action is adjoint, this new Hopf algebra is…
We determine the quantized function algebras associated with various examples of generalized sine-Gordon models. These are quadratic algebras of the general Freidel-Maillet type, the classical limits of which reproduce the lattice Poisson…
We discuss some aspects of the deformed W-algebras W_{q,t}[g]. In particular, we derive an explicit formula for the Kac determinant, and discuss the center when t^2 is a primitive k-th root of unity. The relation of the structure of…
The class of quantum affinizations includes quantum affine algebras and quantum toroidal algebras. In general they have no Hopf algebra structure, but have a "coproduct" (the Drinfeld coproduct) which does not produce tensor products of…
We study commutative associative polynomial operations $\mathbb{A}^n\times\mathbb{A}^n\to\mathbb{A}^n$ with unit on the affine space $\mathbb{A}^n$ over an algebraically closed field of characteristic zero. A classification of such…
With a nilpotent element in a semisimple Lie algebra g one associates a finitely generated associative algebra W called a W-algebra of finite type. This algebra is obtained from the universal enveloping algebra U(g) by a certain Hamiltonian…