## University of Sydney Algebra Seminar

# Gus Lehrer (University of Sydney)

## Friday 25 March, 12:05-12:55pm, Carslaw 175

### The second fundamental theorem of invariant theory for the orthogonal group

I shall explain how the commutant of the classical orthogonal group action on tensor space has a presentation which is obtained from the Brauer algebra by adding one single idempotent relation, which will be explicitly described. This solves a 74 year old mystery. Applications will be given via cellular theory to multiplicity theory in characacteristics other than zero, and to the quantum case at roots of unity. This is joint work with Ruibin Zhang.