JournalsqtVol. 12 , No. 4pp. 705–812

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

  • Abel Lacabanne

    Université Clermont Auvergne, Clermont-Ferrand, France
  • Grégoire Naisse

    Max-Planck Institute for Mathematics, Bonn, Germany
  • Pedro Vaz

    Université Catholique de Louvain, Louvain-la-Neuve, Belgium
Tensor product categorifications, Verma modules and the blob 2-category cover
Download PDF

This article is published open access under our Subscribe to Open model.

Abstract

We construct a dg-enhancement of KLRW algebras that categorifies the tensor product of a universal sl2\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 sl2\mathfrak{sl}_2. From the above we derive a categorification of the blob algebra.

Cite this article

Abel Lacabanne, Grégoire Naisse, Pedro Vaz, Tensor product categorifications, Verma modules and the blob 2-category. Quantum Topol. 12 (2021), no. 4 pp. 705–812

DOI 10.4171/QT/156