Bispectral KP solutions and linearization of CalogeroMoser particle systems
 Alex Kasman
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Rational and soliton solutions of the KP hierarchy in the subgrassmannianGr _{1} are studied within the context of finite dimensional dual grassmannians. In the rational case, properties of the tau function, τ, which are equivalent to bispectrality of the associated wave function, ψ, are identified. In particular, it is shown that there exists a bound on the degree of all time, variables in τ if and only if ψ is a rank one bispectral wave function. The action of the bispectral involution, β, in the generic rational case is determined explicitly in terms of dual grassmannian parameters. Using the correspondence between rational solutions, and particle systems, it is demonstrated that β is a linearizing map of the CalogeroMoser particle system and is essentially the map σ introduced by Airault, McKean and Moser in 1977 [2].
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 Title
 Bispectral KP solutions and linearization of CalogeroMoser particle systems
 Journal

Communications in Mathematical Physics
Volume 172, Issue 2 , pp 427448
 Cover Date
 19950901
 DOI
 10.1007/BF02099435
 Print ISSN
 00103616
 Online ISSN
 14320916
 Publisher
 SpringerVerlag
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 Authors

 Alex Kasman ^{(1)}
 Author Affiliations

 1. Department of Mathematics, Boston University, 02215, Boston, MA, USA