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Rational Cherednik algebras, Hilbert schemes and combinatorics

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Tomasz Przezdziecki
Fri, 2018-03-16 14:15 - 16:00
MPIM Seminar Room

We will discuss the connection between cyclotomic rational Cherednik algebras at t=0 and the Hilbert scheme of points in the plane. In particular, we will explain how the spectrum of the centre of the rational Cherednik algebra is diffeomorphic to a certain component of the Hilbert scheme. Analyzing torus actions we will derive some combinatorial applications such as Bezrukavnikov and Finkelberg's proof of Haiman's conjecture about wreath MacDonald polynomials and a generalization of the q-hook formula.

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