Three lectures on classical integrable systems and gauge field theories
arXiv:0802.3857 · doi:10.1134/S1063779609010067
Abstract
In these lectures I consider the Hitchin integrable systems and their relations with the self-duality equations and the twisted super-symmetric Yang-Mills theory in four dimension follow Hitchin and Kapustin-Witten. I define the Symplectic Hecke correspondence between different integrable systems. As an example I consider Elliptic Calogero-Moser system and integrable Euler-Arnold top on coadjoint orbits of the group GL(N,C) and explain the Symplectic Hecke correspondence for these systems.
36 pages, Lectures given at Advanced Summer School on Integrable Systems and Quantum Symmetries (Prague, June, 2007)
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