2020/01/30 by Laurent Vera, Vera, Laurent
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Black Holes and Theoretical Physics
paper · pdf · doi:10.48550/arxiv.2001.11551
Let U be a quantized enveloping algebra. We consider the adjoint action of an \mathfraksl2-subalgebra of U on a subalgebra of U+ that is maximal integrable for this action. We categorify this representation in the context of quiver Hecke algebras. We obtain an action of the 2-category associated with \mathfraksl2 on a category of modules over certain quotients of quiver Hecke algebras. Our approach is similar to that of Kang-Kashiwara for categorifications of highest weight modules via cyclotomic quiver Hecke algebras. One of the main new features is a compatibility of the categorical action with the monoidal structure, categorifying the notion of derivation on an algebra. As an application of some of our results, we categorify the higher order quantum Serre relations, extending results of Stošić to the non simply-laced case.