Geometry of Higgs bundles over elliptic curves related to automorphisms of simple Lie algebras, Calogero-Moser systems and KZB equations

Abstract

We construct twisted Calogero-Moser (CM) systems with spins as the Hitchin systems derived from the Higgs bundles over elliptic curves, where transitions operators are defined by an arbitrary finite order automorphisms of the underlying Lie algebras. In this way we obtain the spin generalization of the twisted D'Hoker- Phong and Bordner-Corrigan-Sasaki-Takasaki systems. As by product, we construct the corresponding twisted classical dynamical r-matrices and Knizhnik-Zamolodchikov-Bernard equations related to the automorphisms of the Lie algebras.

35 pages + 2 tables

References in corpus (5)

• Characteristic Classes and Integrable Systems for Simple Lie Groups
• Characteristic Classes and Integrable Systems. General Construction
• Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles
• Twisted spin Sutherland models from quantum Hamiltonian reduction
• Quadratic algebras related to elliptic curves

Cited by in corpus (1)

• Noncommutative extensions of elliptic integrable Euler-Arnold tops and Painleve VI equation