Derived superequivalences for spin symmetric groups and odd sl(2)-categorifications

Mark Ebert; Aaron D. Lauda; Laurent Vera

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arXiv · 2203.14153

Derived superequivalences for spin symmetric groups and odd sl(2)-categorifications

Mark Ebert·Aaron D. Lauda·Laurent Vera

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Abstract

We show that actions of the odd categorification of sl(2) induce derived superequivalences analogous to those introduced by Chuang and Rouquier. Using Kang, Kashiwara, and Oh's action of the odd 2-category on blocks of the cyclotomic affine Hecke-Clifford algebra, our equivalences imply that blocks related by a certain affine Weyl group action are derived equivalent. By recent results of Kleshchev and Livesey, we show this implies Broue's abelian defect conjecture for the modular representations of the spin symmetric group.

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Mark Ebert, Aaron D. Lauda, Laurent Vera. 2022-03-26. Derived superequivalences for spin symmetric groups and odd sl(2)-categorifications. https://arxiv.org/abs/2203.14153

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