Quantizations of Hitchin and Beauville-Mukai integrable systems

Details Quantizations of Hitchin and Beauville-Mukai integrable systems Quantizations of Hitchin and Beauville-Mukai integrable systems

2002-09-23

arxiv.org/abs/math/0209294v1

Mathematics

Algebraic Geometry

35 pages

Scientific paper

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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