Related papers: Characteristic Classes of SL(N)-Bundles and Quantu…

In this paper we propose versions of the associative Yang-Baxter equation and higher order $R$-matrix identities which can be applied to quantum dynamical $R$-matrices. As is known quantum non-dynamical $R$-matrices of Baxter-Belavin type…

We propose an algebraic scheme for quantizing the rational Ruijsenaars-Schneider model in the R-matrix formalism. We introduce a special parameterization of the cotangent bundle over GL(N,C). In new variables the standard symplectic…

We introduce an elliptic version of the Grothendieck-Springer sheaf and establish elliptic analogues of the basic results of Springer theory. From a geometric perspective, our constructions specialize geometric Eisenstein series to the…

In this paper, we give the general forms of the minimal $L$ matrix (the elements of the $L$-matrix are $c$ numbers) associated with the Boltzmann weights of the $A_{n-1}^1$ interaction-round-a-face (IRF) model and the minimal representation…

Let X be a smooth projective curve over an algebraically closed field k of characteristic p>0. In this paper we explore the relation between algebraic D-modules on the moduli space $Bun_n$ of vector bundles of rank n on X and coherent…

For any affine Lie algebra ${\mathfrak g}$, we show that any finite dimensional representation of the universal dynamical $R$ matrix ${\cal R}(\lambda)$ of the elliptic quantum group ${\cal B}_{q,\lambda}({\mathfrak g})$ coincides with a…

We construct finite $R$-matrices for the first fundamental representation $V$ of two-parameter quantum groups $U_{r,s}(\mathfrak{g})$ for classical $\mathfrak{g}$, both through the decomposition of $V\otimes V$ into irreducibles…

We study vector bundles with some additional structures on an elliptic curve and show how there are related to the elliptic Ruijsenaars-Schneider model.

We introduce a category O of modules over the elliptic quantum group of sl_N with well-behaved q-character theory. We construct asymptotic modules as analytic continuation of a family of finite-dimensional modules, the Kirillov--Reshetikhin…

In this paper we explain the parallelism in the classification of three different kinds of mathematical objects: (i) Classical r-matrices. (ii) Generalized cohomology theories that have Chern classes for complex vector bundles. (iii)…

A brane construction of an integrable lattice model is proposed. The model is composed of Belavin's R-matrix, Felder's dynamical R-matrix, the Bazhanov-Sergeev-Derkachov-Spiridonov R-operator and some intertwining operators. This…

We introduce the $h$-adic quantum vertex algebras associated with the rational $R$-matrix in types $B$, $C$ and $D$, thus generalizing the Etingof--Kazhdan's construction in type $A$. Next, we construct the algebraically independent…

For a simple complex Lie group G the connected components of the moduli space of G-bundles over an elliptic curve are weighted projective spaces. In this note we will provide a new proof of this result using the invariant theory of…

A theory of characteristic classes of vector bundles and smooth manifolds plays an important role in the theory of smooth manifolds. An investigation of reasonable notions of characteristic classes of singular spaces started since a…

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…

A complete classification of non-affine dynamical quantum $R$-matrices obeying the ${\mathcal G}l_n({\mathbb C})$-Gervais-Neveu-Felder equation is obtained without assuming either Hecke or weak Hecke conditions. More general dynamical…

We study quantum current algebra $\textrm{A}(\overline{R})$ associated with the rational $R$-matrix of $\mathfrak{gl}_N$ and we give explicit formulae for the elements of its center at the critical level. Due to Etingof--Kazhdan's…

We suggest a formula for quantum universal $R$-matrices corresponding to quasitriangular classical $r$-matrices classified by Belavin and Drinfeld for all simple Lie algebras. The $R$-matrices are obtained by twisting the standard universal…

We quantize the coordinate ring of the moduli space of B-bundles on the elliptic curve. Here B is a Borel subgroup of some semisimple Lie group. We construct some representations of these algebras and study intertwining operators for these…

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…