Sam Thelin (Oxford), An algebraic approach to the KZ-functor for rational Cherednik algebras.

Abstract:

Rational Cherednik algebras are certain degenerations of the double affine Hecke algebras introduced by Cherednik to prove Macdonald's constant term conjectures for root systems of Lie algebras. They are also special cases of symplectic reflection algebras as introduced by Etingof and Ginzburg. Rational Cherednik algebras have a triangular decomposition reminiscent of that of the universal enveloping algebra of a finite-dimensional complex semisimple Lie algebra, and they have a category O of representations similar to the Bernstein-Gelfand-Gelfand category O. A crucial tool for studying category O is the Knizhnik-Zamolodchikov functor (KZ-functor for short) introduced by Ginzburg, Guay, Opdam and Rouquier. In this talk, we will discuss a conjecture by Ginzburg and Rouquier on an algebraic description of the KZ-functor, and present some partial results in this direction.