Hostname: page-component-669899f699-rg895 Total loading time: 0 Render date: 2025-04-27T13:41:34.183Z Has data issue: false hasContentIssue false
  • English
  • Français

TRIGONOMETRIC DARBOUX TRANSFORMATIONS AND CALOGERO–MOSER MATRICES

Published online by Cambridge University Press:  01 February 2009

LUC HAINE ,
EMIL HOROZOV  and
PLAMEN ILIEV
LUC HAINE
Affiliation:
Department of Mathematics, Université catholique de Louvain, Chemin du Cyclotron 2, 1348 Louvain-la-Neuve, Belgium e-mail: [email protected]
EMIL HOROZOV
Affiliation:
Department of Mathematics and Informatics, Sofia University, 5 J. Bourchier Boulevard, Sofia 1126, Bulgaria and Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Block 8, 1113 Sofia, Bulgaria e-mail: [email protected]
PLAMEN ILIEV
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332–0160, USA e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We characterize in terms of Darboux transformations the spaces in the Segal–Wilson rational Grassmannian, which lead to commutative rings of differential operators having coefficients which are rational functions of ex. The resulting subgrassmannian is parametrized in terms of trigonometric Calogero–Moser matrices.

Keywords

35Q5337K10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue A , February 2009 , pp. 95 - 106
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

REFERENCES

1.Bakalov, B., Horozov, E. and Yakimov, M., Bäcklund–Darboux transformations in Sato's Grassmannian, Serdica Math. J. 22 (4) (1996), 571–588.Google Scholar
2.Bakalov, B., Horozov, E. and Yakimov, M., Bispectral algebras of commuting ordinary differential operators, Commun. Math. Phys. 190 (1997), 331–373.CrossRefGoogle Scholar
3.Chalykh, O. A. and Nijhoff, F. W., Bispectral rings of difference operators, Russ. Math. Surv. 54 (3) (1999), 644–645.Google Scholar
4.Dickey, L. A., Soliton equations and Hamiltonian systems, Second Edition, Advanced Series in Mathematical Physics 26 (World Scientific Publishing Co., River Edge, NJ, 2003).CrossRefGoogle Scholar
5.Haine, L., KP trigonometric solitons and an adelic flag manifold, SIGMA Symm. Integr. Geom. Meth. Appl. 3 (Paper 015), (2007), 15 pages.Google Scholar
6.Haine, L. and Iliev, P., Commutative rings of difference operators and an adelic flag manifold, Int. Math. Res. Not. 2000 (6) (2000), 281–323.CrossRefGoogle Scholar
7.Iliev, P., Rational Ruijsenaars-Schneider hierarchy and bispectral difference operators, Phys. D 229 (2) (2007), 184–190.CrossRefGoogle Scholar
8.Kasman, A. and Gekhtman, M., Solitons and almost-intertwining matrices, J. Math. Phys. 42 (2001), 3540–3551.CrossRefGoogle Scholar
9.Mukhin, E., Tarasov, V. and Varchenko, A., Bispectral and (gl N, gl M) dualities, discrete versus differential, Adv. Math. 218 (1) (2008), 216–265.CrossRefGoogle Scholar
10.Wilson, G., Bispectral commutative ordinary differential operators, J. Reine Angew. Math. 442 (1993), 177–204.Google Scholar
11.Wilson, G., Collisions of Calogero–Moser particles and an adelic Grassmannian, Invent. Math. 133 (1998), 1–41.CrossRefGoogle Scholar