Semi-Direct Products Involving Sp2n or Spinn with Free Algebras of Symmetric Invariants

Abstract

This is a part of an ongoing project, the goal of which is to classify all semidirect products s = g⋉V such that g is a simple Lie algebra, V is a g-module, and 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.