# 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.

## AMS Subject Classification (1991)

Primary: 17B67

## Content

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