# Jon Brundan (University of Oregon)

## The oriented skein category

I’ll talk about a monoidal category which appeared 30 years ago in work of Turaev on the HOMFLY-PT link invariant. The standard way to understand its representation theory is to use Schur-Weyl duality connecting it to the monoidal category Rep $$U_q(\mathfrak{gl}_n)$$, but it can also be approached directly using a triangular decomposition.