On rank one 2-representations of web categories

Abstract

We classify rank one 2-representations of SL2, GL2 and SO3 web categories. The classification is inspired by similar results about quantum groups, 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.

arXiv comment23 pages, many figures, revision, to appear in Algebr. Comb., comments welcome

References in corpus (23)

• A diagrammatic approach to categorification of quantum groups I
• Webs and quantum skew Howe duality
• Canonical forms for complex matrix congruence and *congruence
• Cell 2-representations of finitary 2-categories
• Complexity of matrix problems
• The Blanchet-Khovanov algebras
• Integral presentations of quantum lattice Heisenberg algebras
• Cellular structures using ${\text{U}}_q$-tilting modules
• Invariant tensors and cellular categories
• Light ladders and clasp conjectures
• Trace decategorification of the Hecke category
• Diagram categories for ${\text{U}}_q$-tilting modules at roots of unity
• Finitary birepresentations of finitary bicategories
• Symmetric webs, Jones-Wenzl recursions and $q$-Howe duality
• Semisimplicity of Hecke and (walled) Brauer algebras
• Tutte chromatic identities from the Temperley-Lieb algebra
• Simple transitive $2$-representations of Soergel bimodules for finite Coxeter types
• Classification of non-Kac compact quantum groups of SU(n) type
• SL2 tilting modules in the mixed case
• Growth rates of the number of indecomposable summands in tensor powers
• On the functoriality of sl(2) tangle homology
• Monoidal categories, representation gap and cryptography
• Sandwich cellularity and a version of cell theory