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Calogero–Moser Systems and Hitchin Systems

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Abstract:

We exhibit the elliptic Calogero–Moser system as a Hitchin system of G-principal Higgs pairs. The group G, though naturally associated to any root system, is not semi-simple. We then interpret the Lax pairs with spectral parameter of d'Hoker and Phong [dP1] and Bordner, Corrigan and Sasaki [BCS1] in terms of equivariant embeddings of the Hitchin system of G into that of GL(N).

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Authors and Affiliations

  1. Centre de Recherches Mathématiques, Université de Montréal and Department of Mathematics,¶McGill University, Montréal, Quebec H3C 3P8, Canada. E-mail: hurtubis@crm.umontreal.ca, , , , , , CA

    J. C. Hurtubise

  2. Department of Mathematics, University of Massachusetts, Amherst, MA 01003, USA.¶E-mail: markman@math.umass.edu, , , , , , US

    E. Markman

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  1. J. C. Hurtubise
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  2. E. Markman
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Received: 8 May 2000 / Accepted: 2 July 2001

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Hurtubise, J., Markman, E. Calogero–Moser Systems and Hitchin Systems. Commun. Math. Phys. 223, 533–552 (2001). https://doi.org/10.1007/s002200100546

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  • DOI: https://doi.org/10.1007/s002200100546

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