Verma Howe duality and LKB representations
Representation Theory
2026-03-30 v3 Geometric Topology
Quantum Algebra
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.
Keywords
Cite
@article{arxiv.2207.09124,
title = {Verma Howe duality and LKB representations},
author = {Abel Lacabanne and Daniel Tubbenhauer and Pedro Vaz},
journal= {arXiv preprint arXiv:2207.09124},
year = {2026}
}
Comments
24 pages, many figures, to appear in New York J. Math., comments welcome