Related papers: Pure braid group actions on category O modules

We find the explicit form of the basic monodromy operators for the case of the quantum group $\mathrm U_q(\mathcal L(\mathfrak{sl}_3))$. Expressions for the quantum Casimir elements of the quantum groups $\mathrm U_q(\mathfrak{gl}_3)$ and…

We prove that any action of a finite dimensional Hopf algebra H on a Weyl algebra A over an algebraically closed field of characteristic zero factors through a group action. In other words, Weyl algebras do not admit genuine finite quantum…

Let A be a finitely generated connected graded k-algebra defined by a finite number of monomial relations. Then there is a finite directed graph, Q, the Ufnarovskii graph of A, for which the categories QGr(A) and QGr(kQ) are equivalent:…

We give a unified construction of quantum groups, q-Boson algebras and quantized Weyl algebras and an action of quantum groups on quantized Weyl algebras. This enables us to give a conceptual proof of the semi-simplicity of the category…

We show that the structure of blocks outside the critical hyperplanes of category O over any symmetrizable Kac-Moody algebra depends only on the corresponding integral Weyl group and its action on the parameters of the Verma modules by…

Let $\mathfrak{g}$ be a symmetrizable Kac-Moody algebra and let $U_q(\mathfrak{g})$ denote the corresponding quantized enveloping algebra. In the present paper we show that quantum symmetric pair coideal subalgebras $B_{c,s}$ of…

We construct a braided analogue of the quantum permutation group and show that it is the universal braided compact quantum group acting on a finite space in the category of $\mathbb{Z}/N\mathbb{Z}$-$\textrm{C}^*$-algebras with a twisted…

We prove that the quantum cluster algebra structure of a unipotent quantum coordinate ring $A_q(\mathfrak{n}(w))$, associated with a symmetric Kac-Moody algebra and its Weyl group element $w$, admits a monoidal categorification via the…

We study the category O of representations of the rational Cherednik algebra A attached to a complex reflection group W. We construct an exact functor, called Knizhnik-Zamolodchikov functor, from O to the category of H-modules, where H is…

In this paper, we give a unified construction of two-parameter quantum groups $U_{r,s}(\mathfrak{g})$, two-parameter Kashiwara algebras $B_{r,s}(\mathfrak{g})$, two-parameter quantized Weyl algebras $W_{r,s}(\mathfrak{g})$ and the action of…

Let $U_q'(\mathfrak{g})$ be a quantum affine algebra of untwisted affine $ADE$ type, and $\mathcal{C}_{\mathfrak{g}}^0$ the Hernandez-Leclerc category of finite-dimensional $U_q'(\mathfrak{g})$-modules. For a suitable infinite sequence…

We construct a braiding operator in terms of the quantum dilogarithm function based on the quantum cluster algebra. We show that it is a q-deformation of the R-operator for which hyperbolic octrahedron is assigned. Also shown is that, by…

As a continuation of \cite{JLO1}, we investigate the quantum virtual Grothendieck ring $\frakK_q(\g)$ associated with a finite dimensional simple Lie algebra $\g$, especially of non-simply-laced type. We establish an isomorphism $\Uppsi_Q$…

We study the classification of group actions on C*-algebras up to equivariant KK-equivalence. We show that any group action is equivariantly KK-equivalent to an action on a simple, purely infinite C*-algebra. We show that a conjecture of…

For non-abelian simple objects in a unitary modular category, the density of their braid group representations, the #P-hard evaluation of their associated link invariants, and the BQP-completeness of their anyonic quantum computing models…

We consider the category of C*-algebras equipped with actions of a locally compact quantum group. We show that this category admits a monoidal structure satisfying certain natural conditions if and only if the group is quasitriangular. The…

We construct a direct sum completion $\mathcal{C}_{\oplus}$ of a given braided monoidal category $\mathcal{C}$ which allows for the rigorous treatment of infinite order simple current extensions of vertex operator algebras as seen in…

Let $G$ be a reductive algebraic group with Lie algebra $\mathfrak{g}$ and $V$ a finite-dimensional representation of $G$. Costello-Gaiotto studied a graded Lie algebra $\mathfrak{d}_{\mathfrak{g}, V}$ and the associated affine Kac-Moody…

We define 2-functors on the categorified quantum group of a simply-laced Kac-Moody algebra that induce Lusztig's internal braid group action at the level of the Grothendieck group.

Let g be a semisimple Lie algebra over an algebraically closed field k of characteristic 0. Let V be a simple finite-dimensional g-module and let y\in V be a highest weight vector. It is a classical result of B. Kostant that the algebra of…