Abstract
We discuss geometrical aspects of different dualities in the integrable systems of the Hitchin type and its various generalizations. It is shown that T duality known in the string theory context is related to the separation of variables procedure in dynamical systems. We argue that there are analogues of S duality as well as mirror symmetry in many-body systems of Hitchin type. The different approaches to double elliptic systems are unified using the geometry behind the Mukai-Odesskii algebra.
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Gorsky, A., Rubtsov, V. (2001). Dualities in Integrable Systems: Geometrical Aspects. In: Pakuliak, S., von Gehlen, G. (eds) Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory. NATO Science Series, vol 35. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0670-5_11
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DOI: https://doi.org/10.1007/978-94-010-0670-5_11
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