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Bispectral Duality of Integrable Particle Systems

Banff International Research Station for Mathematical Innovation and Discovery

Two particle systems are said to be “dual” if the maps that linearize their dynamics are inverses. “Bispectrality", on the other hand, describes the situation in which a function satisfies two eigenvalue equations with the roles of spacial and spectral variables exchanged. Although bispectrality does not initially appear to be dynamical in nature, it turns out that duality manifests itself as bispectrality on both the classical and quantum levels. (For example, the Calogero-Moser system is self-dual since its action-angle map is an involution, and this can be seen either in a symmetry of the eigenfunction of its quantum Hamiltonian or through the appearance of this particle system in the pole dynamics of bispectral solutions of the KP Hierarchy.) This talk will review both old and recent results on this subject and then conclude with a list of associated open problems.

Mathematics; Dynamical systems and ergodic theory; Ordinary differential equations; Dynamical systems

video/mp4

Author affiliation: College of Charleston

2017-01-29

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60038

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/