Abstract
Let C [x] denote the ring of polynomials with complex coefficients in n variables x = (x1,x2,...,xn). We are interested in studying polynomials which remain invariant under the action of a finite matrix group Γ ⊂ GL(Cn). The main result of this chapter is a collection of algorithms for finding a finite set I1, I2,...,Im of fundamental invariants which generate the invariant subring C[x]Γ. 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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© 2008 Springer-Verlag/Wien
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(2008). Invariant theory of finite groups. In: Algorithms in Invariant Theory. Texts and Monographs in Symbolic Computation. Springer, Vienna. https://doi.org/10.1007/978-3-211-77417-5_2
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DOI: https://doi.org/10.1007/978-3-211-77417-5_2
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-77416-8
Online ISBN: 978-3-211-77417-5
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