Categorification of infinite-dimensional $\mathfrak{sl}_2$-modules and braid group 2-actions I: tensor products
Benjamin Dupont,
Grégoire Naisse
Abstract:This is the first part of a series of two papers aiming to construct a categorification of the braiding on tensor products of Verma modules, and in particular of the Lawrence-Krammer-Bigelow representations. In this part, we categorify all tensor products of Verma modules and integrable modules for quantum sl 2 . The categorification is given by derived categories of dg versions of KLRW algebras which generalize both the tensor product algebras of Webster, and the dg-algebras used by Lacabanne, the second auth… Show more
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