Verma Howe duality and LKB representations

Data

• Title: Verma Howe duality and LKB representations
• Authors: Abel Lacabanne, Daniel Tubbenhauer and Pedro Vaz
• arXiv link: https://arxiv.org/abs/2207.09124
• Published in: New York J. Math. 31 (2025), 1507–1542.
• DOI: No DOI

Abstract

We establish a version of Howe duality that involves a tensor product of Verma modules. Surprisingly, this duality leaves the realm of lowest and highest weight modules. We quantize this duality, and as an application, we prove that the (colored higher) LKB representations arise from this duality and use this description to show that they are simple as modules for the braid group and for various of its subgroups, including the pure braid group.

Citation

@article {MR4987728,
    AUTHOR = {Lacabanne, Abel and Tubbenhauer, Daniel and Vaz, Pedro},
     TITLE = {Verma {H}owe duality and {LKB} representations},
   JOURNAL = {New York J. Math.},
  FJOURNAL = {New York Journal of Mathematics},
    VOLUME = {31},
      YEAR = {2025},
     PAGES = {1507--1542},
      ISSN = {1076-9803},
   MRCLASS = {17B10 (17B37 20)},
  MRNUMBER = {4987728},
}