Semi-Direct Products Involving Sp 2 n or Spin n with Free Algebras of Symmetric Invariants
This is a part of an ongoing project, the goal of which is to classify all semi-direct products \({\mathfrak {s}}={\mathfrak g}{\ltimes }V\) 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.