On rank one 2-representations of web categories

Publication date: 3 July 2023

Abstract: We classify rank one 2-representations of SL2, GL2 and SO3 web categories. The classification is inspired by similar results about quantum groups and given by reducing the problem to the classification of bilinear and trilinear forms, and is formulated such that it can be adapted to other web categories.

Has companion code repository: https://github.com/dtubbenhauer/2-representations-of-webs

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47) Monoidal categories, symmetric monoidal categories (18M05) String diagrams and graphical calculi (18M30)

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