Quantum Groups, Deformations, and Geometry

A Conference in Memory of Joseph Donin

I. Loseu - Minimally supported representations of Rational Cherednik algebras and invariants of torus knots

Rational Cherednik algebras were introduced by Etingof and Ginzburg in the beginning of 2000's based on an earlier work of Cherednik, Dunkl and others. Surprisingly, these algebras are related to many objects outside Representation theory: Calogero-Moser integrable systems, Hilbert schemes of points on the plane, Macdonald polynomials, the geometry of plane curves, and invariants of torus knots. In my talk I will discuss a connection to the latter. Namely, I will introduce so called minimally supported representations and discuss their properties and their (conjectural) connection to invariants of torus knots -- the HOMFLY polynomials and the Khovanov-Rozansky homology. The talk is based on a joint work with Etingof and Gorsky, arXiv:1304.3412.