We establish a link between two geometric approaches to the representation theory of rational Cherednik algebras of type A: one based on a noncommutative Proj construction [GS1]; the other involving quantum hamiltonian reduction of an algebra of differential operators [GG]. In the present paper, we combine these two points of view by showing that the process of hamiltonian reduction intertwines...

These are notes for a talk in the MIT-Northeastern Spring 2015 Graduate Representation Theory Seminar. The main source is [BR14].

The Matsuo–Cherednik correspondence is an isomorphism from solutions of Knizhnik–Zamolodchikov equations to eigenfunctions of generalized Calogero–Moser systems associated to Coxeter groups G and a multiplicity function m on their root systems. It is valid for generic values of the spectral parameters, in the complement of the discriminant locus. We extend the Matsuo–Cherednik correspondence co...

We establish a link between two geometric approaches to the representation theory of rational Cherednik algebras of type A: one based on a noncommutative Proj construction [GS1]; the other involving quantum hamiltonian reduction of an algebra of differential operators [GG]. In this paper, we combine these two points of view by showing that the process of hamiltonian reduction intertwines a natu...

We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincaré-Birkhoff-Witt (PBW) type. We ...

1 Mayer J, Boldt J, Schollhorn T, Rohm KD, Mengistu AM, Suttner S. Semi-invasive monitoring of cardiac output by a new device using arterial pressure waveform analysis: a comparison with intermittent pulmonary artery thermodilution in patients undergoing cardiac surgery. Br J Anaesth 2007; 98: 176–82 2 Sander M, Spies CD, Grubitzsch H, Foer A, Muller M, von Heymann C. Comparison of uncalibrated...