Spherical Indecomposable Representations of Lie Superalgebras

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.

44 pages, version published in Journal of Algebra; references added, minor typos corrected, appendix B and table therein removed to reduce length (table will appear in author's PhD thesis)