Представления рациональных алгебр Чередника с минимальным носителем

This talk is based on the joint work with Etingof and Gorsky, arXiv: 1304.3412. We study irreducible representations of Rational Cherednik algebras having minimal support. We establish a number of their properties: Cohen-Macaulayness, relation between characters and colored HOMFLY polynomials, Koszul resolutions, and symmetry. Our motivation mostly comes from a conjectural relation between these representations and knot homology.