2007/01/27 by Luc Haine · 16 citations
Chemistry · Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Combinatorics #Computer science #Dual (grammatical number) #Duality (order theory) #Flag (linear algebra) #Hierarchy #Interpretation (philosophy) #Mathematical analysis #Mathematics #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Property (philosophy) #Pure mathematics #Rank (graph theory) #Trigonometry #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.3842/sigma.2007.015
published in Symmetry Integrability and Geometry Methods and Applications (National Academy of Sciences of Ukraine) · This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
arxiv created 2007/01/27 · openalex publication_date 2007/01/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that the trigonometric solitons of the KP hierarchy enjoy a differentialdifference bispectral property, which becomes transparent when translated on two suitable spaces of pairs of matrices satisfying certain rank one conditions. The result can be seen as a non-self-dual illustration of Wilson's fundamental idea [Invent. Math. 133 (1998), 1-41] for understanding the (self-dual) bispectral property of the rational solutions of the KP hierarchy. It also gives a bispectral interpretation of a (dynamical) duality between the hyperbolic Calogero-Moser system and the rational Ruijsenaars-Schneider system, which was first observed by Ruijsenaars [Comm. Math. Phys. 115 (1988), 127-165].