Calogero-Moser operators and symmetric functions

Martin Hallnas (University of Loughborough)

Tuesday 2nd February, 2010 15:00-16:00 Mathematics Building, room 204

Abstract

Calogero-Moser operators are certain types of partial differential operators that define integrable, and in many cases exactly solved, quantum many-body systems in one space dimension. In work by Chalykh, Feigin, Sergeev and Veselov it has been shown that these operators allow for a certain deformation while preserving integrability. In this talk we will focus on a particular example, corresponding to the rational Calogero-Moser system with harmonic confinement, and discuss how this phenomena can be understood by considering Calogero-Moser operators in infinitely many variables. In particular, this will naturally lead to the introduction of certain symmetric function analogues of the Hermite polynomials.

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