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R-Matrices, Generalized Inverses, and Calogero—Moser—Sutherland Models

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Calogero—Moser— Sutherland Models

Part of the book series: CRM Series in Mathematical Physics ((CRM))

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Abstract

Four results are given that address the existence, ambiguities, and construction of a classical R-matrix given a Lax pair. They enable the uniform construction of R-matrices in terms of any generalized inverse of ad(L). For generic L a generalized inverse (and indeed the Moore-Penrose inverse) is explicitly constructed. The R-matrices are in general momentum dependent and dynamical. We apply our construction to the elliptic Calogero-Moser-Sutherland models associated with gln.

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Authors
  1. H. W. Braden
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Editors and Affiliations

  1. Departamento de Matematicas, Universidad de Chile, Las Palmeras, 3425, Nunoa Santiago, Chile

    Jan Felipe van Diejen

  2. McGill University, James Administration Building, Room 504, Montreal, Quebec, H3A 2T5, Canada

    Luc Vinet

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Braden, H.W. (2000). R-Matrices, Generalized Inverses, and Calogero—Moser—Sutherland Models. In: van Diejen, J.F., Vinet, L. (eds) Calogero—Moser— Sutherland Models. CRM Series in Mathematical Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1206-5_6

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  • DOI: https://doi.org/10.1007/978-1-4612-1206-5_6

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7043-0

  • Online ISBN: 978-1-4612-1206-5

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