Related papers: Raising/lowering maps and modules for the quantum …

We show that the action of universal $R$-matrix of affine $U_qsl_2$ quantum algebra, when $q$ is a root of unity, can be renormalized by some scalar factor to give a well defined nonsingular expression, satisfying Yang-Baxter equation. It…

We study a family of Siegel modular forms that are constructed using Jacobi forms that arise in Umbral moonshine. All but one of them arise as the Weyl-Kac-Borcherds denominator formula of some Borcherds-Kac-Moody (BKM) Lie superalgebras.…

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 study relations between the two-parameter $\U_q(sl(n))$-invariant deformation quantization on $sl^*(n)$ and the reflection equation algebra. The latter is described by a quantum permutation on $\End(\C^n)$ given explicitly. The…

This article is the first of two where we investigate to what extent homotopy invariant, excisive and matrix stable homology theories help one distinguish between the Leavitt path algebras $L(E)$ and $L(F)$ of graphs $E$ and $F$ over a…

Let $L_K(E)$ denote the Leavitt path algebra associated to the finite graph $E$ and field $K$. For any closed path $c$ in $E$, we define and investigate the uniserial, artinian, non-noetherian left $L_K(E)$-module $U_{E,c-1}$. The unique…

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…

We construct finite-dimensional irreducible representations of two quantum algebras related to the generalized Lie algebra $\ssll (2)_q$ introduced by Lyubashenko and the second named author. We consider separately the cases of $q$ generic…

Using free field representation of quantum affine algebra $U_q(\widehat{sl_2})$, we investigate the structure of the Fock modules over $U_q(\widehat{sl_2})$. The analisys is based on a $q$-analog of the BRST formalism given by Bernard and…

We propose a quantum lattice version of Feigin and E. Frenkel's constructions, identifying the KdV differential polynomials with functions on a homogeneous space under the nilpotent part of $\widehat{s\ell}_2$. We construct an action of the…

In this paper, we first review the definition of the novel quantum affine algebra \(U_{\textbf{q}}(\widehat{\mathfrak{sl}}_2)\) of type \(A_{1}^{(1)}\) given in \cite{FHZ, HZhuang}. Furthermore, by introducing \(\Omega\)-invariant…

The factorization of the universal R-matrix corresponding to so called Drinfeld Hopf structure is described on the example of quantum affine algebra $U_q(\hat{sl}_2)$. As a result of factorization procedure we deduce certain differential…

We establish a natural connection of the $q$-Virasoro algebra $D_{q}$ introduced by Belov and Chaltikian with affine Kac-Moody Lie algebras. More specifically, for each abelian group $S$ together with a one-to-one linear character $\chi$,…

To a smooth and proper morphism $\mathcal{X}\to U$ with quasicompact semiseparated target we associate a sheaf in the \'etale topology, which takes an affine $U$-scheme $V$ to the set of $V$-linear semiorthogonal decompositions (of fixed…

We define a family of universal finite-dimensional highest weight modules for affine Lie algebras, we call these Weyl modules. We conjecture that these are the classical limits of the irreducible finite--dimensional representations of the…

We relate a certain category of sheaves of k-vector spaces on a complex affine Schubert variety to modules over the k-Lie algebra (for ch k>0) or to modules over the small quantum group (for ch k=0) associated to the Langlands dual root…

An example of a finite dimensional factorizable ribbon Hopf C-algebra is given by a quotient H=u_q(g) of the quantized universal enveloping algebra U_q(g) at a root of unity q of odd degree. The mapping class group M_{g,1} of a surface of…

The integrable structure of the one-dimensional Hubbard model is based on Shastry's R-matrix and the Yangian of a centrally extended sl(2|2) superalgebra. Alcaraz and Bariev have shown that the model admits an integrable deformation whose…

We construct families of commutative (super) algebra objects in the category of weight modules for the unrolled restricted quantum group $\overline{U}_q^H(\mfg)$ of a simple Lie algebra $\mfg$ at roots of unity, and study their categories…

Let k be a field, Q a finite directed graph, and kQ its path algebra. Make kQ an N-graded algebra by assigning each arrow a positive degree. Let I be an ideal in kQ generated by a finite number of paths and write A = kQ/I. Let QGr A denote…