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A new approach to the representation theory of the partition category

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arxiv 2107.05099 v1 pith:HIYVPA3M submitted 2021-07-11 math.RT

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keywords categorypartitionapproachelementsfunctorsjucys-murphymonoidalreformulation
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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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  1. Diagrammatic Categories which arise from Representation Graphs

    math.CT 2025-02 reject novelty 6.0 of 10

    A construction of diagrammatic categories from McKay quivers is presented, with a conditional equivalence theorem to the monoidal category of irreducible G-modules that rests on an unproven path-basis assumption.

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