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Invariant theory of finite groups

  • Bernd Sturmfels
Part of the Texts and Monographs in Symbolic Computation book series (TEXTSMONOGR)

Abstract

Let C[x] denote the ring of polynomials with complex coefficients in n variables x = (x 1, x 2,…, x n). We are interested in studying polynomials which remain invariant under the action of a finite matrix group Г ⊂ GL(C n). The main result of this chapter is a collection of algorithms for finding a finite set {I 1, I 2,…, I m} of fundamental invariants which generate the invariant subring C[x]Г. These algorithms make use of the Molien series (Sect. 2.2) and the Cohen—Macaulay property (Sect. 2.3). In Sect. 2.4 we include a discussion of invariants of reflection groups, which is an important classical topic. Sections 2.6 and 2.7 are concerned with applications and special cases.

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Copyright information

© Springer-Verlag Wien 1993

Authors and Affiliations

  • Bernd Sturmfels
    • 1
  1. 1.Department of MathematicsCornell UniversityIthacaUSA

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