Abstract.
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.
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Kazarnovski-Krol, A. Matrix elements of vertex operators of the deformed W A n -algebra and the Harish-Chandra solutions to Macdonald's difference equations. Sel. math., New ser. 5, 257 (1999). https://doi.org/10.1007/s000290050049
DOI: https://doi.org/10.1007/s000290050049