Speaker :
 Ruibin Zhang (University of Sydney) 

Title :

Second fundamental theorem of invariant theory for orthogonal and symplectic groups 
Time :
 20121217 (Mon) 14:00  15:00 
Place : 
Room 202, AstroMath. Building 

Abstract: 
The first and second fundamental theorems (FFT and SFT) of classical invariant theory are respectively concerned with generators and relations for invariants of group actions. Let G be the orthogonal group O(V) or the symplectic Sp(V), and let be the algebra of endomorphisms of . The FFT of the invariant theory of G in this setting states that there is a surjective algebra homomorphism from the Brauer algebra of degree r to the subalgebra of invariants in End(). However, the SFT remained elusive in this setting. We will develop an SFT by studying a category of Brauer tangle diagrams, and discuss the generalization of the results to the corresponding quantum groups. This is joint work with Gus Lehrer. 
