Abstract

In this chapter we continue to use invariant theory and algebraic geometry to analyze the regular elements of pseudo-reflection groups. We shall apply the machinery from Chapter 33 to study regular elements of pseudo-reflection groups. It has been demonstrated in §29–5 that, in the case of Euclidean reflection groups, Coxeter elements are regular. The properties studied in this section have already been established for Coxeter elements. We shall be asking in this chapter to what extent certain properties generalize from Coxeter elements to regular elements in arbitrary pseudo-reflection groups. The results of this chapter are taken from Springer [2].

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