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International Conference dedicated to the 60-th birthday of Boris Feigin "Representation Theory and applications to Combinatorics, Geometry and Quantum Physics"
December 13, 2013 11:30–12:20, Moscow, Independent University of Moscow

Representations of the Lie superalgebra $P(n)$ and Brauer algebras with signs

V. V. Serganova
 Video records: Flash Video 405.9 Mb MP4 405.9 Mb

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. 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.
We discuss some properties of this algebra in application to representation theory of $P(n)$ and $P(\infty)$.
We also construct a universal tensor category such that for all n the categories of $P(n)$ modules can be obtained as quotients of this category. In some sense this category is an analogue of the Deligne categories $GL(t)$ and $SO(t)$.