# Centralizers of the superalgebra osp(1|2): the Brauer algebra as a quotient of the Bannai-Ito algebra

## TL;DR

This paper establishes an explicit isomorphism between a quotient of the Bannai-Ito algebra and the Brauer algebra, clarifies the connection with osp(1|2) actions, and proposes a conjecture on centralizers in tensor representations.

## Contribution

It introduces a new explicit isomorphism linking the Bannai-Ito algebra quotient to the Brauer algebra and explores the centralizer structure of osp(1|2) actions.

## Key findings

- Explicit isomorphism between Bannai-Ito quotient and Brauer algebra
- Connection between osp(1|2) action and algebraic structures
- Conjecture on centralizer description in tensor representations

## Abstract

We provide an explicit isomorphism between a quotient of the Bannai--Ito algebra and the Brauer algebra. We clarify also the connection with the action of the Lie superalgebra osp(1|2) on the threefold tensor product of its fundamental representation. Finally, a conjecture is proposed to describe the centralizer of osp(1|2) acting on three copies of an arbitrary finite irreducible representation in terms of a quotient of the Bannai-Ito algebra.