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.

A.L. was supported by a PEPS JCJC grant from INSMI (CNRS). D.T. was supported by the Australian Research Council, and they also like to thank Sydney's architects for not taking cold weather serious. P.V. was supported by the Fonds de la Recherche Scientifique - FNRS under Grant no. MIS-F.4536.19. We also thank Universite Clermont Auvergne for supporting a research visit of P.V. to Clermont-Ferrand.