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Algèbres commutatives d'opérateurs aux q-différences et systèmes de Calogero—Moser

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Iliev, P

We define a subspace Gr(q)(ad) of Sato's Grassmannian Gr, which is a q-deformation of Wilson's adelic Grassmannian Gr(ad). From each plane W is an element of Gr(q)(ad) lye constrict a bispectral commutative algebra A(W)(q) of q-difference operators. The common eigenfunction Psi (x, z) for the operators from A(W)(q) is a q-wave (Baker-Akhiezer) function for a rational solution to a q-deformation of the KP hierarchy. The poles of these solutions are governed by a certain q-deformation of the Calogero-Moser hierarchy. (C) 1999 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 1999
Language Français
Journal information "Comptes rendus de l'Académie des sciences - Series I - Mathematics" - Vol. 329, no. 10, p. 877-882 (1999)
Peer reviewed yes
Publisher Editions Scientifiques Medicales Elsevier (Paris Cedex 15)
issn 0764-4442
Publication status Publié
Affiliation UCL
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Bibliographic reference Iliev, P. Algèbres commutatives d'opérateurs aux q-différences et systèmes de Calogero—Moser. In: Comptes rendus de l'Académie des sciences - Series I - Mathematics, Vol. 329, no. 10, p. 877-882 (1999)
Permanent URL http://hdl.handle.net/2078.1/43807