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Hidden Algebraic Structure of the Calogero—Sutherland Model, Integral Formula for Jack Polynomial and Their Relativistic Analog

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Calogero—Moser— Sutherland Models

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

Abstract

We review some recent results on the Calogero—Sutherland and Ruijsenaars models with emphasis on their algebraic aspects. We give integral formulas for excited states (Jack and Macdonald polynomials) of these models, their relations with the Virasoro singular vectors and its q-analog and obtain free boson realization for level one elliptic affine Lie algebra.

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Authors
  1. Hidetoshi Awata
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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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Awata, H. (2000). Hidden Algebraic Structure of the Calogero—Sutherland Model, Integral Formula for Jack Polynomial and Their Relativistic Analog. 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_2

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  • DOI: https://doi.org/10.1007/978-1-4612-1206-5_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7043-0

  • Online ISBN: 978-1-4612-1206-5

  • eBook Packages: Springer Book Archive

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