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The representation theory of Brauer categories I: triangular categories (2006.04328v2)
Published 8 Jun 2020 in math.RT
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.