Harmonic locus and Calogero-Moser spaces | Integrable System Lunch Seminar

Abstract

We study the harmonic locus consisting of the monodromy-free Schroedinger operators withrational potential and quadratic growth at infinity. lt is known after Oblomkov, that it can be identifiedwith the set of all partitions via Wronskian map for Hermite polynomials. We show that the harmoniclocus can also be identified with the subset of the Calogero-Moser space introduced by Wilson,which is invariant under the symplectic action of C*. As a corollary, for the multiplicity-free part ofthelocuswe effectively solve the inverse problem for the Wronskian map by describing partition interms of the spectrum of the corresponding Moser's matrix.

The talk is based on a joint work with Giovanni Felder.