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Tensor product categorifications, Verma modules and the blob 2-category (2005.06257v2)
Published 13 May 2020 in math.QA and math.RT
Abstract: We construct a dg-enhancement of KLRW algebras that categorifies the tensor product of a universal $\mathfrak{sl}_2$ Verma module and several integrable irreducible modules. When the integrable modules are two-dimensional, we construct a categorical action of the blob algebra on derived categories of these dg-algebras which intertwines the categorical action of $\mathfrak{sl}_2$. From the above we derive a categorification of the blob algebra.
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