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Akinori Nishino Yasushi Komori Hideaki Ujino Miki Wadati 《Studies in Applied Mathematics》2002,108(4):399-425
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. 相似文献
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Optical Review - Dynamics of water content in a biological tissue is an important information of a biological activity. However, although the conventional measurement method measures the total... 相似文献
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For the quantum Calogero-Moser model, we present the following two results. First, it has a set of conserved operators which are involutive. This proves the integrability of the model. Second, the Lax operator gives a list of new operators (boost operators). The conserved operators and the boost operators constitute the U(1)-current algebra. 相似文献
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Miki Wadati Akinori Nishino Hideaki Ujino Yasushi Komori 《Journal of statistical physics》2001,102(3-4):1049-1064
We study in an algebraic manner the symmetric basis of the Calogero model and the non-symmetric basis of the corresponding Calogero model with distinguishable particles. The Rodrigues formulas are presented for the polynomial parts of both bases. The square norm of the non-symmetric basis is evaluated. Symmetrization of the non-symmetric basis reproduces the symmetric basis and enables us to calculate its square norm. 相似文献
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