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Symmetrization of Nonsymmetric Macdonald Polynomials and Macdonald's Inner Product Identities
Author(s) -
Nishino Akinori,
Komori Yasushi,
Ujino Hideaki,
Wadati Miki
Publication year - 2002
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.01431
Subject(s) - symmetrization , macdonald polynomials , koornwinder polynomials , askey–wilson polynomials , mathematics , pure mathematics , orthogonal polynomials , eigenvalues and eigenvectors , classical orthogonal polynomials , mathematical analysis , physics , quantum mechanics
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.