### GRT at home Seminar

**Wille Liu, Université de Paris**

* Knizhnik--Zamolodchikov functor for degenerate double affine Hecke algebras*

Organizer's time: 2020-06-30 16:00 Europe/Paris

Duration: 1 hour 30 minutes

Access information: zoom: 842 5923 2669

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The Knizhnik--Zamolodchikov (KZ) equations of 2-dimensional Conformal Field Theory have several incarnations. The famous double affine Hecke algebra (DAHA) was introduced by Cherednik in order to study these equations. The degenerate (trigonometric) version dDAHA of DAHA controls a family of KZ equations on the Riemann sphere. Via the monodromy of the KZ equation, Varagnolo and Vasserot have constructed in 2004 a so-called KZ functor from the category of a dDAHA to the affine Hecke algebra of the same type. This functor had previously been introduced for rational Cherednik algebras by Ginzburg, Guay, Opdam and Rouquier (GGOR) in 2003 and had received a lot of attention in that context. The case of the trigonometric KZ functor has received comparatively less attention.

In this talk, I will give a purely algebraic construction of the trigonometric KZ functor for dDAHA and I will present several results which are analogous to those of GGOR for dDAHA. I will also introduce a generalization for quiver Hecke algebras.

Video: here

Slides: here

Submitted by: Schiffmann