On the Veselov-Felder reconstruction formula in the theory of Calogero-Sutherland operators
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Matsuo  and Cherednik  proposed an elegant construction connecting the solutions of generalized Knizhnik-Zamolodchikov (KZ) equations with the eigenfunctions of Calogero-Sutherland operators associated with the same root system. Considering rational KZ equations, Veselov  and Felder  simplified the arguments used in [1, 2] and derived the reconstruction formula for the root system An−1. This gives the solution of the KZ equation in terms of eigenfunctions of the Calogero operator. In this paper, for any reduced and irreducible root system, we directly verify the Matsuo-Cherednik statement for the connection of solutions to KZ equations to the eigenfunctions of Calogero-Sutherland operators. We extend the Felder-Veselov reconstruction formula to these root systems.
KeywordsRoot System Reconstruction Formula Irreducible Root System
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