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The representation theory of Brauer categories I: triangular categories

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arxiv 2006.04328 v2 pith:LUQ7KOZ7 submitted 2020-06-08 math.RT

Steven V Sam , Andrew Snowden This is my paper · ORCID
classification math.RT
keywords categorybrauercategoriestriangulartheoryabstractsadmitalgebra
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This is the first in a series of papers in which we study representations of the Brauer category and its allies. We define a general notion of triangular category that abstracts key properties of the triangular decomposition of a semisimple complex Lie algebra, and develop a highest weight theory for them. We show that the Brauer category, the partition category, and a number of related diagram categories admit this structure.

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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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