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The Representation Theory of Brauer Categories I: Triangular Categories

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Abstract

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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  • 24 August 2022

    In this article the ‘Communicated by’ note was incorrect and should have read ‘Communicated by Henning Krause’.

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  1. Department of Mathematics, University of California, San Diego, CA, USA

    Steven V Sam

  2. Department of Mathematics, University of Michigan, Ann Arbor, MI, USA

    Andrew Snowden

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Communicated by Henning Krause.

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SS was supported by NSF Grant DMS-1812462. AS was supported by NSF Grants DMS-1453893.

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Sam, S.V., Snowden, A. The Representation Theory of Brauer Categories I: Triangular Categories. Appl Categor Struct 30, 1203–1256 (2022). https://doi.org/10.1007/s10485-022-09689-7

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