相关论文: A Kohno-Drinfeld theorem for quantum Weyl groups

Let $\mathfrak g$ be a simple Lie algebra with Cartan subalgebra $\mathfrak h$ and Weyl group $W$. We build up a graded map $(\mathcal H\otimes \bigwedge\mathfrak h\otimes \mathfrak h)^W\to (\bigwedge \mathfrak g\otimes \mathfrak…

Let V(KG) be a normalised unit group of the modular group algebra of a finite p-group G over the field K of p elements. We introduce a notion of symmetric subgroups in V(KG) as subgroups invariant under the action of the classical…

Let $\mathfrak{g}$ be a symmetrizable Kac-Moody algebra, $U_q(\mathfrak{g})$ its quantum group, and $U_q(\mathfrak{k}) \subset U_q(\mathfrak{g})$ a quantum symmetric pair subalgebra determined by a Lie algebra automorphism $\theta$. We…

We describe a new geometric model for the Hochschild cohomology of Soergel bimodules based on the monodromic Hecke category studied earlier by the first author and Yun. Moreover, we identify the objects representing individual Hochschild…

By means of the notions of cross product algebras of the theory of quantum groups, in the context of classical Hopf algebra structures, we deduce some known structures of Weyl algebras type (as the Drinfeld quantum double, the restricted…

Chiral conformal blocks in a rational conformal field theory are a far going extension of Gauss hypergeometric functions. The associated monodromy representations of Artin's braid group capture the essence of the modern view on the subject,…

For every semi-simple Lie algebra one can construct the Drinfeld-Jimbo algebra U. This algebra is a deformation Hopf algebra defined by generators and relations. To study the representation theory of U, Drinfeld used the KZ-equations to…

Let $\left( H,R\right) $ be a finite dimensional semisimple and cosemisimple quasi-triangular Hopf algebra over a field $k$. In this paper, we give the structure of irreducible objects of the Yetter-Drinfeld module category ${}…

Generalising work of Calaque-Enriquez-Etingof, we construct a universal KZB connection D_R for any finite (reduced, crystallographic) root system R. D_R is a flat connection on the regular locus of the elliptic configuration space…

We construct an explicit bundle with flat connection on the configuration space of n points of a complex curve. This enables one to recover the `formality' isomorphism between the Lie algebra of the prounipotent completion of the pure braid…

In this paper, we extend the Drinfeld current realization of quantum affine algebras $U_q(\hat {\gg})$ and of the Yangians in several directions: we construct current operators for non-simple roots of ${\gg}$, define a new braid group…

In this article, we study the multiparameter second quantum Weyl algebra at roots of unity. In this setting, the algebra is a polynomial identity (PI) algebra, and the dimension of its simple modules is bounded above by its PI degree. We…

We consider a connected compact Lie group K acting on a symplectic manifold M such that a moment map m exists. A pull-back function via m Poisson commutes with all K-invariants. Guillemin-Sternberg raised the problem to find a converse. In…

We generalize the basic results of Vinberg's \theta-groups, or periodically graded reductive Lie algebras, to fields of good positive characteristic. To this end we clarify the relationship between the little Weyl group and the (standard)…

In this note we propose a construction of the Hopf algebra of a complex analog of devided powers of the Weyl generators of a semisimple simply-laced quantum group. Here we consider the generators as positive, self-adjoint operators. In…

We obtain the Plancherel theorem for the quotient of a simple Lie group of real rank one by a convex-cocompact discrete subgroup and its consequences for the spectrum of locally invariant differential operators on bundles over Kleinian…

This is the first of a series of papers devoted to certain pairs of commuting nilpotent elements in a semisimple Lie algebra that enjoy quite remarkable properties and which are expected to play a major role in Representation theory. The…

Let $U_q'(\mathfrak{g})$ be an arbitrary quantum affine algebra of either untwisted or twisted type, and let $\mathscr{C}_{\mathfrak{g}}^0$ be its Hernandez-Leclerc category. We denote by $\mathsf{B}$ the braid group determined by the…

This paper is a continuation of the series of papers "Quantization of Lie bialgebras (QLB) I-V". We show that the image of a Kac-Moody Lie bialgebra with the standard quasitriangular structure under the quantization functor defined in…

In this paper we use the Etingof-Kazhdan quantization of Lie bi-superalgebras to investigate some interesting questions related to Drinfeld-Jimbo type superalgebra associated to a Lie superalgebra of classical type. It has been shown that…