# Seminarium z teorii mnogości i topologii

### czwartek 18:00 sala 510 Instytut Matematyki UJK

Seminarium 17.05.2018

On the representation theory of periplectic Lie superalgebras and affine $VW$ supercategory
Mee Seong Im
(Army Research Laboratory, Supercomputing Research Center, Aberdeen Proving Ground, MD 21005)

I will first give an introduction to the construction of what is known as periplectic Lie superalgebras $p(n)$. A construction of the affine $VW$ supercategory arose from our study of the representation theory of periplectic Lie superalgebras. Letting $V$ to be a superspace with $\mathbb{Z}/2\mathbb{Z}$-grading and $M$ to be a $p(n)$-module, we construct a super version of the degenerate BMW algebra in the process of examining higher Schur-Weyl duality for the tensor product of $M$ with finitely-many copies of $V$. I will discuss affine VW superalgebras and their center, and the affine $VW$ supercategory and its connection to Brauer supercategory. This is joint with M. Balagovic, Z. Daugherty, I. Entova-Aizenbud, I. Halacheva, J. Hennig, G. Letzter, E. Norton, V. Serganova, and C. Stroppel.

 Opieka naukowa: prof. Taras Banakh prof. Wiesław Kubiś Organizacja: dr Joanna Garbulińska-Węgrzyn dr Magdalena Nowak