Matrix elements of vertex operators of the deformed W A n -algebra and the Harish-Chandra solutions to Macdonald's difference equations

• A. Kazarnovski-Krol ^[1]
  1. [1] Rutgers University

     Rutgers University

     City of New Brunswick, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 5, Nº. 2, 1999, págs. 257-301
• Idioma: inglés
• DOI: 10.1007/s000290050049
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• Resumen

  • In this paper we prove that certain matrix elements of vertex operators of the deformed W A n -algebra satisfy Macdonald's difference equations and form a natural (n + 1)!-dimensional space of solutions. These solutions are the analogues of the Harish-Chandra solutions of the radial parts of the Laplace-Casimir operators on noncompact Riemannian symmetric spaces G/K with prescribed asymptotic behavior. We obtain formulas for analytic continuation of our Harish-Chandra type solutions as a consequence of braiding properties (obtained earlier by Y. Asai, M. Jimbo, T. Miwa, and Y. Pugay) of certain vertex operators of the deformed W A n -algebra.