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

Data

• Title: Tensor product categorifications, Verma modules and the blob $2$-category
• Authors: Abel Lacabanne, Grégoire Naisse and Pedro Vaz
• arXiv link: https://arxiv.org/abs/2005.06257
• Published in: Quantum Topol. 12 (2021), no. 4, pp. 705–812
• DOI: 10.4171/QT/156

Abstract

We construct a dg-enhancement of Webster’s tensor product algebras that categorifies the tensor product of a universal $\mathfrak{sl}_2$ Verma module and several integrable irreducible modules. We show that the blob algebra acts via endofunctors on derived categories of such dg-enhanced algebras in the case when the integrable modules are two-dimensional. This action intertwines with the categorical action of $\mathfrak{sl}_2$. From the above we derive a categorification of the blob algebra.

Citation

@article {MR4321215,
    AUTHOR = {Lacabanne, Abel and Naisse, Gr\'egoire and Vaz, Pedro},
     TITLE = {Tensor product categorifications, {V}erma modules and the blob
              2-category},
   JOURNAL = {Quantum Topol.},
  FJOURNAL = {Quantum Topology},
    VOLUME = {12},
      YEAR = {2021},
    NUMBER = {4},
     PAGES = {705--812},
      ISSN = {1663-487X,1664-073X},
   MRCLASS = {18N25 (20G42)},
  MRNUMBER = {4321215},
MRREVIEWER = {Luz\ Adriana\ Mej\'ia Casta\~no},
       DOI = {10.4171/qt/156},
       URL = {https://doi.org/10.4171/qt/156},
}