相关论文: Evaluation-type deformed modules over the quantum …

We define analytic $R$-groups for affine Hecke algebras, and prove the analog of the Knapp-Stein Dimension Theorem. As a corollary we prove that the commutant algebra of a unitary principal series representation is isomorphic to the complex…

The general formula for the universal R-matrix for quantized nontwisted affine algebras by Khoroshkin and Tolstoy is applied for zero central charge highest weight modules of the quantized affine algebras. It is shown how the universal…

We provide geometric constructions of modules over the graded Cherednik algebra $\mathfrak{H}^{gr}_\nu$ and the rational Cherednik algebra $\mathfrak{H}^{rat}_\nu$ attached to a simple algebraic group $\mathbb{G}$ together with a pinned…

In this paper, we prove the categories of lower bounded twisted modules of positive integer levels for simple vertex operator algebras associated with affine Lie algebras and general automorphisms are semisimple, using the twisted…

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 continue our exercises with the universal $R$-matrix based on the Khoroshkin and Tolstoy formula. Here we present our results for the case of the twisted affine Kac--Moody Lie algebra of type $A^{(2)}_2$. Our interest in this case is…

The irreducible components of the variety of all modules over the preprojective algebra and MV cycles both index bases of the universal enveloping algebra of the positive part of a semisimple Lie algebra canonically. To relate these two…

An explicit isomorphism between the $R$-matrix and Drinfeld presentations of the quantum affine algebra in type $A$ was given by Ding and I. Frenkel (1993). We show that this result can be extended to types $B$, $C$ and $D$ and give a…

We construct a vertex representation for the quantum toroidal algebra through the quantum general linear algebra. Using a new realization of the quantum general linear algebra we construct vertex operators for root vectors on the basic…

We prove that the Khovanov-Lauda-Rouquier algebras $R_\al$ of type $A_\infty$ are (graded) affine cellular in the sense of Koenig and Xi. In fact, we establish a stronger property, namely that the affine cell ideals in $R_\al$ are generated…

We construct and investigate the structure of the Khovanov-Lauda-Rouquier algebras $R$ and their cyclotomic quotients $R^\lambda$ which give a categrification of quantum generalized Kac-Moody algebras. Let $U_\A(\g)$ be the integral form of…

The quantum deformation of the Jordanian twist F_qJ for the standard quantum Borel algebra U_q(B) is constructed. It gives the family U_qJ(B) of quantum algebras depending on parameters x and h. In a generic point these algebras represent…

We study a certain family of finite-dimensional simple representations over quantum affine superalgebras associated to general linear Lie superalgebras, the so-called fundamental representations: the denominators of rational $R$-matrices…

Let $\CC^0_{\g}$ be the category of finite-dimensional integrable modules over the quantum affine algebra $U_{q}'(\g)$ and let $R^{A_\infty}\gmod$ denote the category of finite-dimensional graded modules over the quiver Hecke algebra of…

The search for elliptic quantum groups leads to a modified quantum Yang-Baxter relation and to a special class of quasi-triangular quasi Hopf algebras. This paper calculates deformations of standard quantum groups (with or without spectral…

Let $\fg$ be a simple finite-dimensional complex Lie algebra with a Cartan subalgebra $\fh$ and Weyl group $W$. Let $\fg_n$ denote the Lie algebra of $n$-jets on $\fg$. A theorem of Rais and Tauvel and Geoffriau identifies the centre of the…

Let g be a semi-simple Lie algebra, and let g^ be the corresponding affine Kac-Moody algebra. Consider the category of g^-modules at the critical level, on which the action of the Iwahori subalgebra integrates to algebraic action of the…

We provide a unified approach, via deformations of incidence algebras, to several important types of representations with finiteness conditions, as well as the combinatorial algebras which produce them. We show that over finite dimensional…

Let us consider a finite set of pairs consisting of good $U'_q(g)$-modules and invertible elements. The distribution of poles of normalized R-matrices yields Khovanov-Lauda-Rouquier algebras We define a functor from the category of…

We study a class of quantized enveloping algebras, called twisted Yangians, associated with the symmetric pairs of types B, C, D in Cartan's classification. These algebras can be regarded as coideal subalgebras of the extended Yangian for…