# Tensor product representations for orthosymplectic Lie superalgebras

## Authors

Georgia Benkart, Chanyoung Lee Shader and Arun Ram

## Status

Research Report 96-1
Date: January 1996

## Abstract

We derive a general result about commuting actions on certain objects in braided rigid monoidal categories. This enables us to define an action of the Brauer algebra on the tensor space V^tensor-k ($V^{\otimes k}$) which commutes with the action of the orthosymplectic Lie superalgebra spo(V) and the orthosymplectic Lie color algebra spo(V,beta).

We use the Brauer algebra action to compute maximal vectors in V^tensor-k and to decompose V^tensor-k into a direct sum of submodules T^lambda. We compute the characters of the modules T^lambda, give a combinatorial description of these characters in terms of tableaux, and model the decomposition of V^tensor-k into the submodules T^lambda with a Robinson-Schensted-Knuth type insertion scheme.

## Key phrases

Lie algebras. representations. algebraic combinatoric.

Primary: 17B67

## Content

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