Related papers: On a super-analog of the Schur-Weyl Duality

We establish explicit isomorphisms of two seemingly-different algebras, and their Schur algebras, arising from the centralizers of two different type B Weyl group actions in Schur-like dualities. We provide a presentation of the geometric…

In this article, we provide a comprehensive characterization of invariants of classical Lie superalgebras from the super-analog of the Schur-Weyl duality in a unified way. We establish $\mathfrak{g}$-invariants of the tensor algebra…

We obtain Schur-Weyl dualities in which the algebras, acting on both sides, are semigroup algebras of various symmetric inverse semigroups and their deformations.

Let $U_q(\mathfrak{g})$ be the quantized superalgebra of $\mathfrak{g}=\mathfrak{gl}(k_1|\ell_1)\oplus\cdots\oplus\mathfrak{gl}(k_m|\ell_m)$ and $H_{m,n}(q,\mathbf{Q})$ the cyclotomic Hecke algebra of type $G(m,1,n)$. We define a right…

Let A_k denote the twisted group algebra of the symmetric group S_k, whose representations correspond to the nonlinear projective representations of S_k. We establish a duality relation between A_k and a Lie superalgebra q(n), sometimes…

The Schur-Weyl duality, which started as the study of the commuting actions of the symmetric group $S_d$ and $\mathrm{GL}(n,\mathbb{C})$ on $V^{\otimes d}$ where $V=\mathbb{C}^n$, was extended by Drinfeld and Jimbo to the context of the…

Schur-Weyl duality concerns the actions of $\text{GL}_{n}(\mathbb{C})$ and $S_{k}$ on tensor powers of the form $V^{\otimes k}$ for an $n$-dimensional vector space $V$. There are rich histories within representation theory, combinatorics,…

We use a unified elementary approach to prove the second part of classical, mixed, super, and mixed super Schur-Weyl dualities for general linear groups and supergroups over an infinite ground field of arbitrary characteristic. These…

Degenerating the quantum queer Schur superalgebra ${\mathcal{Q}_q(n,r; R)}$ to the case $q=1$, the queer Schur superalgebra ${\mathcal{Q}(n,r)}$ is obtained. In this article, we reconstruct the universal enveloping algebra…

We give a geometric realization of the symmetric algebra of the tensor space $C^n \bigotimes C^m$ together with the action of the dual pair $(gl_n, gl_m)$ in terms of lagrangian cycles in the cotangent bundles of certain varieties. We…

Schur--Weyl--Jones duality establishes the connection between the commuting actions of the symmetric group $S_{n}$ and the partition algebra $P_{k}(n)$ on the tensor space $\left(\mathbb{C}^n\right)^{\otimes k}.$ We give a refinement of…

The classical case of Schur--Weyl duality states that the actions of the group algebras of $GL_n$ and $S_d$ on the $d^{th}$-tensor power of a free module of finite rank centralize each other. We show that Schur--Weyl duality holds for…

We develop and study the generalization of rational Schur algebras to the super setting. Similar to the classical case, this provides a new method for studying rational supermodules of the general linear supergroup $GL(m|n)$. Furthermore,…

Let $V^{\otimes n}$ be the $n$-fold tensor product of a vector space $V.$ Following I. Schur we consider the action of the symmetric group $S_n$ on $V^{\otimes n}$ by permuting coordinates. In the `super' ($\Bbb Z_2$ graded) case…

In both ${\cal N}=1$ and ${\cal N}=2$ supersymmetry, it is known that $\mathsf{Sp}(2n, {\mathbb R})$ is the maximal duality group of $n$ vector multiplets coupled to chiral scalar multiplets $\tau (x,\theta) $ that parametrise the Hermitian…

We determine the finite-dimensional simple modules for two-parameter quantum groups corresponding to the general linear and special linear Lie algebras gl_n and sl_n, and give a complete reducibility result. These quantum groups have a…

We describe the action of the infinite-dimensional Lie algebra $W_{1+\infty}$ and its B-type analogue on Schur and Schur Q-functions, respectively, using formal distributions framework. We observe an interesting self-duality property…

We give a $q$-analogue of Howe duality associated to a pair $(\mf{g},G)$, where $\mf{g}$ is an orthosymplectic Lie superalgebra and $G=O_\ell, Sp_{2\ell}$. We define explicitly {commuting actions} of a quantized enveloping algebra of…

Considering the general linear Lie superalgebra $\mathfrak{gl}(m|n)=\mathfrak{gl}(m|n)_{\bar{\bar 0}}\oplus \mathfrak{gl}(m|n)_{\bar{\bar 1}}$ over $\mathbb{C}$, we first formulate a super version of Vust theorem associated with a principal…

We prove an integral version of the Schur--Weyl duality between the specialized Birman--Murakami--Wenzl algebra $B_n(-q^{2m+1},q)$ and the quantum algebra associated to the symplectic Lie algebra sp_{2m}. In particular, we deduce that this…