Speaker: Vera Serganova, UC Berkeley.
Abstract:
The “strange” Lie superalgebra P(n) is the algebra of endomorphisms of an (n|n)-dimensional vector space V equipped with a non-degenerate odd symmetric form. Representations of P(n) in tensor powers of V are not completely reducible. The centralizer of the P(n)-action in the k-th tensor power of V is given by a certain analogue of the Brauer algebra.Using this algebra one can construct a pseudo-abelian tensor category P-rep, which is a natural analogue of the Deligne categories GL(t)-rep and SO(t)-rep.
Then we construct an abelian tensor category C which satisfy certain universal properties with respect to the categories of representations of P(n) for all n. We discuss combinatorial properties of C and its relationship with P-rep.