Schur-Weyl duality for the Brauer algebra and the ortho-symplectic Lie superalgebra

TL;DR

This paper establishes a Schur-Weyl duality between the Brauer algebra and the ortho-symplectic Lie superalgebra, providing a new algebraic connection in representation theory.

Contribution

It provides a proof of Schur-Weyl duality linking the Brauer algebra with the ortho-symplectic Lie superalgebra, expanding understanding of their relationship.

Findings

Proof of Schur-Weyl duality between Brauer algebra and $ ext{osp}(V)$

New insights into the representation theory of Lie superalgebras

Enhanced algebraic framework connecting Brauer algebra and superalgebra

Abstract

We give a proof of a Schur-Weyl duality statement between the Brauer algebra and the ortho-symplectic Lie superalgebra $\mathfrak{osp}(V)$.