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Seminar

GRTA seminar: Stabilization of representations of periplectic Lie superalgebras March 27, 2018 (03:30 PM PDT - 04:30 PM PDT)
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Location: MSRI: Simons Auditorium
Speaker(s) Inna Entova-Aizenbud (Ben Gurion University of the Negev)
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This is a report on work in progress, joint with V. Serganova.

Vector superspaces are \Z/2-graded vector spaces with the Koszul sign rule, which means that a sign appears every time one swaps two "odd" vectors. This allows one to talk about Lie superalgebras, and to study their (super) representations. Given a vector superspace V=\C^{n|n} with an odd (parity-changing) non-degenerate symmetric pairing V \otimes V \to \C, we can consider the periplectic Lie superalgebra p(n) of endomorphisms preserving such a pairing. The category of (super) representations of p(n) is a non-semisimple tensor category, and has interesting abelian structure. I will describe the construction of a certain limit of such categories when n goes to infinity, called the Deligne category Rep P. This limit reflects nice stabilization phenomena for representations of p(n), but also has a nice universal property which I will explain in the talk.

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