Tensor product categorifications, Verma modules and the blob 2-category

Abstract

We construct a dg-enhancement of KLRW algebras that categorifies the tensor product of a universal ${\mathfrak{sl}}_2$ Verma module and several integrable irreducible modules. When the integrable modules are two-dimensional, we construct a categorical action of the blob algebra on derived categories of these dg-algebras which intertwines the categorical action of ${\mathfrak{sl}}_2$. From the above we derive a categorification of the blob algebra.

v2, 88 pages, reviewed version

References in corpus (3)

• Categorified skew Howe duality and comparison of knot homologies
• An approach to categorification of Verma modules
• Schur-Weyl duality, Verma modules, and row quotients of Ariki-Koike algebras

Cited by in corpus (1)

• Categorification of infinite-dimensional ${\mathfrak{sl}}_2$-modules and braid group 2-actions I: tensor products