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Quantizations of Hitchin and Beauville-Mukai integrable systems

B. Enriquez·V. Rubtsov
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Abstract

Spectral transformation is known to set up a birational morphism between the Hitchin and Beauville-Mukai integrable systems. The corresponding phase spaces are: (a) the cotangent bundle of the moduli space of bundles over a curve C, and (b) a symmetric power of the cotangent surface T^*(C). We conjecture that this morphism can be quantized, and we check this conjecture in the case where C is a rational curve with marked points and rank 2 bundles. We discuss the relation of the resulting isomorphism of quantized algebras with Sklyanin's separation of variables.

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B. Enriquez, V. Rubtsov. 2002-09-23. Quantizations of Hitchin and Beauville-Mukai integrable systems. https://arxiv.org/abs/math/0209294

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