Invariant Theory of Finite Groups

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Geometric BackgroundAlgebraic Geometry: dual point of viewx ∈ V ↔ (X i − x i |i = 1, · · · ,n) A maximal idealV := max − spec(A)Geometric objects:max − spec(A G ) = V//G, "categorical quotient".Invariant Theory of Finite Groups – p. 6/2
Invariant Theory of Finite Groups – p. 7/2Geometric SetupA := affine algebra over field F = F;V := max − spec A, corresponding affine variety;G group of automorphisms on A withring of invariants A G := {a ∈ A | g(a) = a ∀ g ∈ G}.
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Page 18 and 19: ExamplesSymmetric polynomials:G :=

Invariant Theory of Finite Groups

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