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On Some Quadratic Algebras: Jucys—Murphy and Dunkl Elements

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Calogero—Moser— Sutherland Models

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

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Abstract

We study some quadratic algebras that appeared in low- dimensional topology and Schubert calculus. We introduce Jucys—Murphy elements in the braid algebra and in the pure braid group, as well as Dunkl elements in the extended affine braid group. Relationships between the Dunkl elements, Dunkl operators and Jucys-Murphy elements are described.

On leave from Steklov Mathematical Institute, St. Petersburg, Russia.

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Authors
  1. Anatol N. Kirillov
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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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Kirillov, A.N. (2000). On Some Quadratic Algebras: Jucys—Murphy and Dunkl Elements. 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_16

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  • DOI: https://doi.org/10.1007/978-1-4612-1206-5_16

  • 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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