Construction of invariants (Q1174670)

Let \(G\) be a connected reductive group over \(\mathbb{C}\), \(V\) a finite dimensional \(\mathbb{C}\)-vector space, and \(\rho: G\to GL(V)\) a rational representation of \(G\). A triplet \((G,\rho,V)\) is called a ``prehomogeneous vector space'' if \(V\) has an open \(G\)-orbit, and called ``irreducible'' if \(\rho\) is an irreducible representation. In this paper, the author constructs irreducible relative invariants for irreducible prehomogeneous vector spaces. This paper makes a nice contribution to Invariant Theory.