Constructing invariant polynomials via tschirnhaus transformations

Abstract

The technique of using Tschirnhaus transformations to generate invariants was used successfully in the theory of binary quantics. These transformations led to systems of semi-invariants, called protomorphs, which then were used to construct invariants, themselves [2;Chapter X]

In this chapter, we extend this method of protomorphs to semi-simple algebraic groups defined over an algebraically closed field k. The basic theorem is proved in (1.4). This theorem is then applied to the construction of invariants in Section 2. In Section 3, we review the classical example.