Calogero-Moser pairs and the Airy and Bessel bispectral involutions
Mitchell Rothstein
TL;DR
This paper provides explicit formulas for the Airy and Bessel bispectral involutions using Calogero-Moser pairs and discusses the Hamiltonian structure of the poles' motion in these operators.
Contribution
It introduces explicit formulas for bispectral involutions via Calogero-Moser pairs and analyzes their Hamiltonian dynamics.
Findings
Explicit formulas for Airy and Bessel involutions
Hamiltonian structure of pole motion analyzed
Connection between bispectral involutions and Calogero-Moser pairs
Abstract
Explicit formulae are given for the Airy and Bessel bispectral involutions, in terms of Calogero-Moser pairs. Hamiltonian structure of the motion of the poles of the operators is discussed.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons