The integral Schur-Weyl-Sergeev duality

TL;DR

This paper explores the classical limit of quantum queer superalgebras, reconstructs the universal enveloping algebra of the queer Lie superalgebra, and provides a detailed explanation of the Schur-Weyl-Sergeev duality over integers.

Contribution

It reconstructs the universal enveloping algebra of the queer Lie superalgebra from the queer Schur superalgebra and offers a new perspective on the Schur-Weyl-Sergeev duality.

Findings

Reconstruction of ${U({rak{q}_n})}$ from ${ ext{Q}(n,r)}$

Explanation of Schur-Weyl-Sergeev duality over $ ext{Z}$

Connection between quantum and classical queer superalgebras

Abstract

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 ${U({\mathfrak{q}_n})}$ of the queer Lie superalgebra ${\mathfrak{q}_n}$ via ${\mathcal{Q}(n,r)}$, and achieve another explanation of the Schur-Weyl-Sergeev duality. Finally, we depict the Schur-Weyl-Sergeev duality over $\mathbb{Z}$.