The representation theory of Brauer categories I: triangular categories

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.

53 pages

References in corpus (5)

• Introduction to twisted commutative algebras
• Uniformly Presented Vector Spaces
• The Temperley-Lieb categories and skein modules
• Sp-equivariant modules over polynomial rings in infinitely many variables
• Spin representations and centralizer algebras for the Spinor groups

Cited by in corpus (5)

• Sp-equivariant modules over polynomial rings in infinitely many variables
• Stable representation theory: beyond the classical groups
• A new approach to the representation theory of the partition category
• Brauer diagrams, modular operads, and a graphical nerve theorem for circuit algebras
• Graded triangular bases