# Manchester Geometry Seminar 2014/2015

**Thursday 16 April 2015. ** *The Frank Adams Room (Room 1.212), the Alan Turing Building. 4.15pm*
##
Invariants and Representations of the "Strange" Lie Superalgebras

Arkady Vaintrob (University of Oregon)

`vaintrob@uoregon.edu`

Strange Lie superalgebras (superalgebras of series $P$ and $Q$), unlike the other
basic Lie superalgebras (for example $gl(m|n)$ or $osp(m|2n)$), have an odd invariant
bilinear form and do not have an even one. This makes the study of their representations
quite different from the classical story.
We will describe two diagrammatically defined ${\mathbb Z}_2$-graded tensor categories
which act on tensor products of natural representations of $P(n)$ and $Q(n)$ and
provide analogues of the Schur-Weyl duality for the superalgebras $P(n)$ and $Q(n)$.
The endomorphism superalgebras of objects in these categories serve as versions
of the Brauer algebras from the classical invariant theory.