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- W2884142041 abstract "We study stabilization of finite-dimensional representations of the periplectic Lie superalgebras $mathfrak{p}(n)$ as $n to infty$. The paper gives a construction of the tensor category $Rep(underline{P})$, possessing nice universal properties among tensor categories over the category $mathtt{sVect}$ of finite-dimensional complex vector superspaces. First, it is the envelope of the Deligne category corresponding to the periplectic Lie superalgebra, in the sense of arXiv:1511.07699. Secondly, given a tensor category $mathcal{C}$ over $mathtt{sVect}$, exact tensor functors $Rep(underline{P})longrightarrow mathcal{C}$ classify pairs $(X, omega)$ in $mathcal{C}$ where $omega: X otimes X to Pi mathbf{1}$ is a non-degenerate symmetric form and $X$ not annihilated by any Schur functor. The category $Rep(underline{P})$ is constructed in two ways. The first construction is through an explicit limit of the tensor categories $Rep(mathfrak{p}(n))$ ($ngeq 1$) under Duflo-Serganova functors. The second construction (inspired by P. Etingof) describes $Rep(underline{P})$ as the category of representations of a periplectic Lie supergroup in the Deligne category $mathtt{sVect} boxtimes Rep(underline{GL}_t)$. An upcoming paper by the authors will give results on the abelian and tensor structure of $Rep(underline{P})$." @default.
- W2884142041 created "2018-08-03" @default.
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- W2884142041 date "2018-07-25" @default.
- W2884142041 modified "2023-09-27" @default.
- W2884142041 title "Deligne categories and the periplectic Lie superalgebra" @default.
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