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.

中文翻译：

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张量产品分类、Verma 模块和 blob 2 类

我们构建了 KLRW 代数的 dg 增强，它对通用 $\mathfrak{sl}_2$ Verma 模块和几个可积不可约模块的张量积进行分类。当可积模块是二维时，我们在这些 dg 代数的派生类别上构建 blob 代数的分类动作，该分类动作与 $\mathfrak{sl}_2$ 的分类动作交织在一起。从上面我们推导出 blob 代数的分类。