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Department of Mathematics Seminar

Speaker: Professor Yin Chen, Northeast Normal University, China

Title: An Introduction to the Invariant Theory of Finite Groups

Abstract: Let W be a faithful n-dimensional representation of a finite group G over a field F. Let W* denote the dual space of W. We multiplicatively extend the action of G on W* to an action of G on the symmetric algebra F[W]:=S(W*) on W*. The invariant ring F[W]G:={f\in F[W] : \sigma (f)=f,\forall \sigma\in G} is the main object of study in algebraic invariant theory. In this talk, I will present a quick introduction to the nonmodular invariant theory of finite groups, including Chevalley-Shephard-Todd's theorem, Molien's formula, and Cohen-Macaulayness of the invariant rings.