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Actions of sl_2 on algebras appearing in categorification

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arxiv 2103.00048 v2 pith:EINW6EQ5 submitted 2021-02-26 math.RT

Ben Elias , You Qi This is my paper · ORCID
classification math.RT
keywords categorificationmathfrakalgebrasappearactionactionsaddressappearing
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abstract

We prove that many of the recently-constructed algebras and categories which appear in categorification can be equipped with an action of $\mathfrak{sl}_2$ by derivations. The $\mathfrak{sl}_2$ representations which appear are filtered by tensor products of coverma modules. In a future paper, we will address the implications of the $\mathfrak{sl}_2$ structure for categorification.

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  1. Remarks on some infinitesimal symmetries of Khovanov--Rozansky homologies in finite characteristic

    math.GT 2024-12 conditional novelty 6.0 of 10

    A p-differential algebra argument reproves base point independence for characteristic-p Khovanov-Rozansky homology and yields new sl2-symmetry consequences for link homology.

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