Ringel duals of Brauer algebras via super groups

TL;DR

This paper establishes a duality between Brauer algebras and representations of orthosymplectic super groups, providing new proofs for invariant theory results and extending them to positive characteristic cases.

Contribution

It proves that Brauer algebras are Ringel dual to categories of super group representations, offering novel algebraic proofs and extending classical invariant theory results.

Findings

Brauer algebra is Ringel dual to orthosymplectic super group representations.

New algebraic proofs for invariant theory theorems over complex numbers.

Extension of invariant theory results to positive characteristic cases.

Abstract

We prove that the Brauer algebra, for all parameters for which it is quasi-hereditary, is Ringel dual to a category of representations of the orthosymplectic super group. As a consequence we obtain new and algebraic proofs for some results on the fundamental theorems of invariant theory for this super group over the complex numbers and also extend them to some cases in positive characteristic. Our methods also apply to the walled Brauer algebra in which case we obtain a duality with the general linear super group, with similar applications.