# 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)