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KP Trigonometric Solitons and an Adelic Flag Manifold
Symmetry, integrability and geometry: methods and applications, Tome 3 (2007) Cet article a éte moissonné depuis la source Math-Net.Ru

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We show that the trigonometric solitons of the KP hierarchy enjoy a differential-difference 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].
Keywords: Calogero–Moser type systems; bispectral problems. 
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Luc Haine. KP Trigonometric Solitons and an Adelic Flag Manifold. Symmetry, integrability and geometry: methods and applications, Tome 3 (2007). http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a14/

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