Related papers: Schur--Weyl duality for twin groups

Let $V$ be the two-dimensional simple module and $M$ be a projective Verma module for the quantum group of $\mathfrak{sl}_2$ at generic $q$. We show that for any $r\ge 1$, the endomorphism algebra of $M\otimes V^{\otimes r}$ is isomorphic…

The theory of Nichols algebras of diagonal type is known to be closely related to that of semisimple Lie algebras. In this paper the connection between both theories is made closer. For any Nichols algebra of diagonal type invertible…

For polynomial representations of $GL_n$ of a fixed degree, H. Krause defined a new internal tensor product using the language of strict polynomial functors. We show that over an arbitrary commutative base ring $k$, the Schur functor…

In \cite{FMX19}, it is proved that the convolution algebra of top Borel-Moore homology on Steinberg variety of type $B/C$ realizes $U(sl_n^{\theta})$, where $sl_{n}^{\theta}$ is the fixed point subalgebra of involution on $sl_n$. So top…

We show that quantum Schur-Weyl duality leads to Markov duality for a variety of asymmetric interacting particle systems. In particular, we consider three cases: (1) Using a Schur-Weyl duality between a two-parameter quantum group and a…

The problem of quantum equivalence between non-linear sigma models related by Abelian or non-Abelian T-duality is studied in perturbation theory. Using the anomalous Ward identity for Weyl symmetry we derive a relation between the Weyl…

We show how the tools of modern algebraic combinatorics -- representation theory, Murphy elements, and particularly Schur--Weyl duality -- can be used to give an explicit orthonormal basis of eigenfunctions for a "curiously slowly mixing…

Let $V$ be a simple vertex operator algebra containing a rank $n$ Heisenberg vertex algebra $H$ and let $C=\text{Com}\left( {H}, {V}\right)$ be the coset of ${H}$ in ${V}$. Assuming that the representation categories of interest are vertex…

We exhibit a correspondence between subcategories of modules over an algebra and sub-bimodules of the dual of that algebra. We then prove that the semisimplicity of certain such categories is equivalent to the existence of a Peter-Weyl…

The integral formulae pertaining to the unitary group $\mathsf{U}(d)$ have been comprehensively reviewed, yielding fresh results and innovative proofs. Central to the derivation of these formulae lies the employment of Schur-Weyl duality, a…

We consider the finite Weyl groups of classical type -- $W(A_{r})$ for $r \geq 1$, $W(B_{r}) = W(C_{r})$ for $r \geq 2$, and $W(D_{r})$ for $r \geq 4$ -- as supergroups in which the reflections are of odd superdegree. Viewing the…

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 note we describe a seemingly new approach to the complex representation theory of the wreath product $G\wr S_d$ where $G$ is a finite abelian group. The approach is motivated by an appropriate version of Schur-Weyl duality. We…

After reviewing classical Schur-Weyl duality, we present some other contexts which enjoy similar features, relating to Brauer algebras and classical groups.

It was recently understood that one can identify a chiral algebra in any four-dimensional N=2 superconformal theory. In this note, we conjecture the full set of generators of the chiral algebras associated with the T_n theories. The…

We establish a duality relation between one of the twisted group algebras of the hyperoctahedral groupf H_k and a Lie superalgebra q(n_0) \oplus q(n_1) for any integers k and n_0, n_1, where q(n_0) and q(n_1) denote the ``queer''…

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…

Let $G$ be a complex linear algebraic group, $\mathfrak{g}=\Lie(G)$ its Lie algebra and $e\in\mathfrak{g}$ a nilpotent element. Vust's theorem says that in case of $G=\GL(V)$, the algebra $\mbox{End}_{G_e}(V^{\otimes d})$, where $G_e\subset…

We study irreducible spherical unitary representations of the Drinfeld double of a $q$-deformation of a connected simply connected compact Lie group, which can be considered as a quantum analogue of the complexification of the Lie group. In…

In this note, we investigate a kind of double centralizer property for general linear supergroups. For the super space $V=\mathbb{K}^{m\mid n}$ over an algebraically closed field $\mathbb{K}$ whose characteristic is not equal to $2$, we…