Symmetrization of Nonsymmetric Macdonald Polynomials and Macdonald's Inner Product Identities |
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| Authors: | Akinori Nishino Yasushi Komori Hideaki Ujino Miki Wadati |
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| Institution: | University of Tokyo,; Gunma College of Technology |
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| Abstract: | We study the Macdonald polynomials that give eigenstates of some quantum many-body system with long-range interactions. Scalar products of the nonsymmetric Macdonald polynomials are algebraically evaluated through their Rodrigues-type formulas. We present a new proof of Macdonald's inner product identities without recourse to the shift operators; that is, we calculate square norms of the Macdonald polynomials through Weyl-symmetrization of those of the nonsymmetric Macdonald polynomials. |
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