Calogero-Moser systems and Hitchin systems
arXiv:math/9912161 · doi:10.1007/s002200100546
Abstract
We exhibit the elliptic Calogero-Moser system as a Hitchin system of G-principal Higgs pairs. The group G, though naturally associated to any root system, is not semi-simple. We then interpret the Lax pairs with spectral parameter of [dP1] and [BSC1] in terms of equivariant embeddings of the Hitchin system of G into that of GL(N).
22 pages, Plain Tex
Cited by in corpus (11)
- A discrete variational identity on semi-direct sums of Lie algebras
- The Dijkgraaf-Vafa prepotential in the context of general Seiberg-Witten theory
- Characteristic Classes of SL(N)-Bundles and Quantum Dynamical Elliptic R-Matrices
- Quantum Lax pairs via Dunkl and Cherednik operators
- Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
- Inozemtsev System as Seiberg-Witten Integrable system
- Duality and Modularity in Elliptic Integrable Systems and Vacua of N=1* Gauge Theories
- Donagi-Markman cubic for the generalised Hitchin system
- The Lax pairs for elliptic C_n and BC_n Ruijsenaars-Schneider models and their spectral curves
- Self-duality and scattering map for the hyperbolic van Diejen systems with two coupling parameters (with an appendix by S. Ruijsenaars)
- Geometry of Higgs bundles over elliptic curves related to automorphisms of simple Lie algebras, Calogero-Moser systems and KZB equations