Tensor product categorifications, Verma modules and the blob 2-category. (English) Zbl 1484.18022
Summary: 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.
MSC:
| 18N25 | Categorification |
| 20G42 | Quantum groups (quantized function algebras) and their representations |
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