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

Iliev, P
(1999) Comptes rendus de l’Académie des sciences - Series I - Mathematics — Vol. 329, n° 10, p. 877-882 (1999)

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  • Iliev, P
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Abstract
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.
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Iliev, P. (1999). Algèbres commutatives d’opérateurs aux q-différences et systèmes de Calogero—Moser. Comptes rendus de l’Académie des sciences - Series I - Mathematics, 329(10), 877-882. https://doi.org/10.1016/S0764-4442(00)87492-3 (Original work published 1999)