Symmetrization of Nonsymmetric Macdonald Polynomials and Macdonald's Inner Product Identities
Copyright policy )Symmetrization of Nonsymmetric Macdonald Polynomials and Macdonald's Inner Product Identities
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.
- University of Tokyo Japan
Many-body theory; quantum Hall effect, Groups and algebras in quantum theory and relations with integrable systems, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)
Many-body theory; quantum Hall effect, Groups and algebras in quantum theory and relations with integrable systems, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)
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