Date & Time: Wednesday, August 28, 2013, 15:30-17:30.
Venue: Room 216
Title: Invariant theory of classical groups
Speaker: Wilberd van der Kallen, Utrecht University
Abstract: We will discuss the invariant theory of classical groups in this series. Let a group $G$ act linearly on a finite dimensional complex vector space $V$. It is natural to ask for the $G$-invariant complex valued polynomial functions on $V$. These functions form a ring in a natural way. The two fundamental theorems in invariant theory of $G$ give generators for this ring as a complex algebra and the relations amongst these generators. As an example, the symmetric group $S_n$ acts by permuting a basis of $C^n$ and the corresponding invariants are generated as a polynomial ring by the elementary symmetric functions. So the generators are the elementary symmetric functions and there are no relations amongst them. Our aim in this lecture series is to understand the invariants for the natural action of $GL(V)$ on $V$ and on related vector spaces. If there is time, we will also study the analogous theorems for the orthogonal and symplectic groups.
This is the fifth lecture in the series of six lectures.