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)

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.