Related papers: Schur-Weyl duality for $U_{v,t}(sl_{n})$

We introduce a new elliptic quantum toroidal algebra U_{q,\kappa,p}(g_tor) associated with an arbitrary toroidal algebra g_tor. We show that U_{q,\kappa,p}(g_tor) contains two elliptic quantum algebras associated with a corresponding affine…

Let $U'_q(\mathfrak{g})$ be a twisted affine quantum group of type $A_{N}^{(2)}$ or $D_{N}^{(2)}$ and let $\mathfrak{g}_{0}$ be the finite-dimensional simple Lie algebra of type $A_{N}$ or $D_{N}$. For a Dynkin quiver of type…

A description of all the irreducible representations of generalized quantum doubles associated to skew pairings of semisimple Hopf algebras is given. In particular a description of the irreducible representations of semisimple Drinfeld…

This is the second part of the article [math.KT/0408094]. In the first paper, we used the underlying coalgebra structure to develop a cyclic theory. In this paper we define a dual theory by using the algebra structure. We define a cyclic…

After establishing a geometric Schur-Weyl duality in a general setting, we recall this duality in type A in the finite and affine case. We extend the duality in the affine case to positive parts of the affine algebras. The positive parts…

In the present work, we study Yetter-Drinfeld algebras over a pairing of multiplier Hopf algebras. Our main motivation is the construction of a self-dual theory of (C*-)algebraic quantum transformation groupoids. Instead of the standard…

The loop Hecke algebra is a generalization of the Hecke algebra to the loop braid group, introduced by Damiani, Martin and Rowell. We give a new presentation of the loop Hecke algebra provided a mild condition on the parameter and give a…

Let $\left( W,\sigma \right) $ be a symplectic vector space and let $% T:W\rightarrow W$ be a linear map that satisfies a certain condition of non-degeneracy. We define the Schur multiplier $\omega _{\sigma ,T}$ on $W$. To this multiplier…

We explicate relations among the Gelfand--Graev modules for central covers, the Euler--Poincar\'e polynomial of the Arnold--Brieskorn manifold, and the quantum affine Schur--Weyl duality. These three objects and their relations are dictated…

In this article we use a parametrized version of the FRT construction to construct two new coquasitriangular Hopf algebras. The first one, $\widehat{SL_q(2)}$, is a quantization of the coordinate ring on affine $SL(2)$. We show that there…

A natural extension of the Hopf-cyclic cohomology, with coefficients, is introduced to encompass topological Hopf algebras. The topological theory allows to work with infinite dimensional Lie algebras. Furthermore, the category of…

We show that we can release the rigidity of the skew Howe duality process for ${\mathfrak sl}_n$ knot invariants by rescaling the quantum Weyl group action, and recover skein modules for web-tangles. This skew Howe duality phenomenon can be…

We construct homomorphic images of $su(n,n)^{\mathbb C}$ in Weyl Algebras ${\mathcal H}_{2nr}$. More precisely, and using the Bernstein filtration of ${\mathcal H}_{2nr}$, $su(n,n)^{\mathbb C}$ is mapped into degree $2$ elements with the…

We provide an analog of the Drinfeld quantum double construction in the context of crossed Hopf group coalgebras introduced by Turaev. We prove that, provided the base group is finite, the double of a semisimple crossed Hopf group coalgebra…

We introduce the notion of standard multipartitions and establish a one-to-one correspondence between standard multipartitions and irreducible representations with integral weights for the affine Hecke algebra of type A with a parameter q…

The subalgebra of diagonal elements of a quantum matrix group has been conjectured by Daniel Krob and Jean-Yves Thibon to be isomorphic to a cubic algebra, coined the quantum pseudo-plactic algebra. We present a functorial approach to the…

Drinfeld doubles of finite subgroups of SU(2) and SU(3) are investigated in detail. Their modular data - S, T and fusion matrices - are computed explicitly, and illustrated by means of fusion graphs. This allows us to reexamine certain…

Let $(A,\alpha)$ be a finite-dimensional Hom-Hopf algebra. In this paper we mainly construct the Drinfel'd double $D(A)=(A^{op}\bowtie A^{\ast},\alpha\otimes(\alpha^{-1})^{\ast})$ in the setting of Hom-Hopf algebras by two ways, one of…

We give a diagrammatic presentation in terms of generators mod relations of the representation category of $U_q(\mathfrak{sl}_n)$. More precisely, we produce all the relations among $\rm{SL}_n$-webs, thus describing the full subcategory…

Let $\mathbf{G}$ be a reductive group and $\mathbf{X}$ a spherical $\mathbf{G}$-variety over a local non-archimedean field $\mathbb{F}$. We denote by $S(\mathbf{X}(\mathbb{F}))$ the Schwartz-functions on $\mathbf{X}(\mathbb{F})$. In this…