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arXiv · 2107.05099

A new approach to the representation theory of the partition category

Jonathan Brundan·Max Vargas
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Abstract

We explain a new approach to the representation theory of the partition category based on a reformulation of the definition of the Jucys-Murphy elements introduced originally by Halverson and Ram and developed further by Enyang. Our reformulation involves a new graphical monoidal category, the affine partition category, which is defined here as a certain monoidal subcategory of Khovanov's Heisenberg category. We use the Jucys-Murphy elements to construct some special projective functors, then apply these functors to give self-contained proofs of results of Comes and Ostrik on blocks of Deligne's category Rep(S_t).

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BibTeXRIS

Jonathan Brundan, Max Vargas. 2021-07-11. A new approach to the representation theory of the partition category. https://doi.org/10.1016/j.jalgebra.2022.03.010

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