Semi-direct products involving $S{p}_{2n}$ or $Spi{n}_n$ with free algebras of symmetric invariants

Abstract

This is a part of an ongoing project, the goal of which is to classify all semi-direct products $\mathfrak{s}=\mathfrak{g}⋉V$ such that $\mathfrak{g}$ is a simple Lie algebra, $V$ is a $\mathfrak{g}$-module, and $\mathfrak{s}$ has a free algebra of symmetric invariants. In this paper, we obtain such a classification for the representations of the orthogonal and symplectic algebras.

arXiv comment30 pages