In this chapter we study the equivariant theory of arrangements. Let GL(V) denote the general linear group of V. Suppose G ⊆ GL(V) is a finite linear group and A is an arrangement which is stable under the action of G. We assume that the order of G is not divisible by the characteristic of the field 𝕂. Section 6.1 contains definitions, examples, and generalities about the action of G on the polynomial algebra S and on the S-modules Der𝕂 (S) and Ω[V]. We also study the action of G on the algebra A(A) and on the cohomology ring H*(M) in this section.
KeywordsCoxeter Group Reflection Group Basic Derivation Basic Invariant Discriminant Locus
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