Invariant Theory of Finite Groups
Invariant Theory of Finite Groups
Invariant Theory of Finite Groups
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<strong>Invariant</strong> <strong>Theory</strong> <strong>of</strong> <strong>Finite</strong> <strong>Groups</strong> – p. 9/2NotationFrom now on always: G finite groupV a finite dimensional FG - module,V ∗ dual module with basis x 1 , · · · ,x n ,A = Sym(V ∗ ) ∼ = F[x 1 , · · · ,x n ] =: F[V ], polynomial ring;A G := {a ∈ A | g(a) = a, ∀g ∈ G}, (N 0 − graded)ring <strong>of</strong> polynomial invariants.left/ right - action:g·a := a ·g −1 .
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