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arXiv · 0802.3857

Three lectures on classical integrable systems and gauge field theories

M. Olshanetsky
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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.

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M. Olshanetsky. 2008-02-26. Three lectures on classical integrable systems and gauge field theories. https://doi.org/10.1134/s1063779609010067

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