Spherical Indecomposable Representations of Lie Superalgebras

TL;DR

This paper classifies all spherical indecomposable representations of classical and exceptional Lie superalgebras, providing detailed structural information and computations relevant to supersymmetric polynomial functions.

Contribution

It offers a comprehensive classification of spherical indecomposable representations for Lie superalgebras, including stabilizers, symmetric algebras, and Borel subalgebras, with explicit computations.

Findings

Classification of spherical indecomposable representations

Structural descriptions of stabilizers and symmetric algebras

Explicit computation of polynomials on the supersphere

Abstract

We present a classification of all spherical indecomposable representations of classical and exceptional Lie superalgebras. We also include information about stabilizers, symmetric algebras, and Borels for which sphericity is achieved. In one such computation, the symmetric algebra of the standard module of $\mathfrak{osp}(m|2n)$ is computed, which in particular gives the representation-theoretic structure of polynomials on the complex supersphere.