Verma Howe duality and LKB representations

Tubbenhauer, Daniel;Dos Santos Santana Forte Vaz, Pedro;Lacabanne, Abel
(2025) New York Journal of Mathematics — Vol. 31, p. 1507-1542 (2025)

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Abstract
We establish a version of quantum Howe duality with two general linear quantum enveloping algebras that involves a tensor product of Verma modules. 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 various subgroups of the braid group, including the pure braid group.
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Tubbenhauer, D., Dos Santos Santana Forte Vaz, P., & Lacabanne, A. (2025). Verma Howe duality and LKB representations. New York Journal of Mathematics, 31, 1507-1542. https://hdl.handle.net/2078.5/269643 (Original work published 2025)