## University of Sydney Algebra Seminar

# Oded Yacobi (University of Sydney)

## Friday 13 March, 12:05-12:55pm, Place: Carslaw 375

### Invariant theory and (quantum) polynomial functors

### Classical (GL(n),GL(m))-duality is a central result in invariant theory. Its proof is based on a simple geometric fact: the subvariety of full-rank mxn matrices is dense in the affine space of all mxn matrices. Various generalisations of GL(n), such as the quantum group GL_q(n) or the super Lie group GL(m|n), also have corresponding duality theorems. Lacking the geometric setting, these theorems rely on ingredients such as the quantum Borel-Weil theorem or Sergeev duality.

In this talk I will first explain a simple proof of the duality theorem using projective generators in the category of strict polynomial functors. This same proof applies in the super and quantum contexts as well, and in the second part of the talk I will focus on the quantum polynomial functors, recently defined in joint work with Jiuzu Hong.