Multiplicity-free super vector spaces

TL;DR

This paper classifies pairs of semisimple groups and super vector spaces where the super symmetric algebra decomposes into multiplicity-free components, advancing understanding of symmetry and representation theory in super vector spaces.

Contribution

It provides a complete classification of multiplicity-free super vector spaces under the action of connected semisimple groups, a novel result in superalgebra representation theory.

Findings

Classification of pairs (G,V) with multiplicity-free super symmetric algebra

Identification of conditions for multiplicity-free decomposition

Extension of classical multiplicity-free theory to super vector spaces

Abstract

Let $V$ be a complex finite dimensional super vector space with an action of a connected semisimple group $G$. We classify those pairs $(G,V)$ for which all homogeneous components of the super symmetric algebra of $V$ decompose multiplicity-free.