| Résume | Braided module categories are module categories over braided monoidal categories equipped with extra structure providing an action of the braid group of the annulus on endomorphism spaces. In this talk, I will define a small braiding on an inclusion of monoidal categories, which provides a braiding between objects in these categories. Small braidings give certain tensor ideals the canonical structure of a braided module category. Quantum groups are a natural source of small braidings, and from this we construct concrete examples of braided module categories and quantum moment maps. I will outline how we plan to use these examples in skein-theoretic realisations of double affine Hecke algebras and certain modules thereof. Based on joint work-in-progress with Ingo Runkel and Volker Schomerus. |
