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An Introduction to the Invariant Theory of Finite Groups

Department of Mathematics, Wilfrid Laurier University

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.

Date

Monday, Nov. 26, 2018

Time

4 p.m. - 4:50 p.m.

Location

LH3058 (Lazaridis Hall, Room 3058)