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Universal tensor categories via representation theory of supergroups

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Vera Serganova
U. California, Berkeley
Tue, 2017-06-20 15:00 - 16:00
MPIM Lecture Hall

For each of the four series of classical supergroups $GL(m|n)$, $OSP(m|n)$, $P(n)$ and $Q(n)$ we construct universal symmetric monoidal rigid categories by taking certain inverse limits . In the first two cases these categories are abelian envelopes of the Deligne categories $GL(t)$ and $O(t)$ (when t is an integer) while for $P$ and $Q$ we obtain some new tensor categories. We also show that the categories in question are highest weight (in the sense of Cline, Parshall and Scott) using interaction with representations of the  ind (super)groups $GL(\infty)$, $O(\infty)$, $P(\infty)$, and $Q(\infty)$. (Most of the talk is based on joint work with I. Entova-Aizenbud and V. Hinich.)

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