Separating coordinates for the generalized Hitchin systems and the classical r-matrices

Authors
Hurtubise, JC Kjiri, M
Citation
Jc. Hurtubise et M. Kjiri, Separating coordinates for the generalized Hitchin systems and the classical r-matrices, COMM MATH P, 210(2), 2000, pp. 521-540
Citations number
24
Categorie Soggetti
Physics
Journal title
COMMUNICATIONS IN MATHEMATICAL PHYSICS
ISSN journal
00103616 → ACNP
Volume
210
Issue
2
Year of publication
2000
Pages
521 - 540
Database
ISI
SICI code
0010-3616(200003)210:2<521:SCFTGH>2.0.ZU;2-M
Abstract
We exhibit natural Darboux coordinates for the generalized Hitchin systems studied by Bottacin and Markman. These systems are defined on spaces of sta ble pairs consisting of a vector bundle and a form-valued meromorphic endom orphism of the bundle. In special cases (genus zero, genus one), the bundle s are:rigid and one has the rational, trigonometric and elliptic Gaudin sys tems. Explicit formulae are given in these cases.