A Remark on the Fourier Pairing and the Binomial Formula for the Macdonald Polynomials
Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 2, pp. 62-68.

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We concisely and directly prove that the interpolation Macdonald polynomials are orthogonal with respect to the Fourier pairing and briefly discuss immediate applications of this fact, in particular, to the symmetry of the Fourier pairing and to the binomial formula.
Keywords: Macdonald polynomials, Fourier pairing
Mots-clés : binomial formula.
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A. Yu. Okounkov. A Remark on the Fourier Pairing and the Binomial Formula for the Macdonald Polynomials. Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 2, pp. 62-68. http://geodesic.mathdoc.fr/item/FAA_2002_36_2_a5/

[1] Cherednik I., “Macdonald's evaluation conjectures and difference Fourier transform”, Invent. Math., 122:1 (1995), 119–145 | DOI | MR | Zbl

[2] Cherednik I., “Nonsymmetric Macdonald polynomials”, Intern. Math. Res. Notices, 1995, 483–515 | DOI | MR | Zbl

[3] Knop F., “Symmetric and non-symmetric quantum Capelli polynomials”, Comment. Math. Helv., 72 (1997), 84–100 | DOI | MR | Zbl

[4] Knop F., Combinatorics and invariant theory of multiplicity free spaces, arXiv: /math.RT/0106079

[5] Knop F., Sahi S., “Difference equations and symmetric polynomials defined by their zeros”, Internat. Math. Res. Notices, 1996, no. 10, 473–486 | DOI | MR | Zbl

[6] Macdonald I. G., Symmetric Functions and Hall Polynomials, 2nd ed., Oxford University Press, 1995 ; Makdonald I., Simmetricheskie funktsii i mnogochleny Kholla, Mir, M., 1985 | MR | Zbl | MR

[7] Macdonald I. G., Symmetric Functions and Orthogonal Polynomials, Dean Jacqueline B. Lewis Memorial Lectures presented at Rutgers University, New Brunswick, NJ, University Lecture Series, 12, Amer. Math. Soc., Providence, RI, 1998 | MR | Zbl

[8] Okounkov A., “(Shifted) Macdonald polynomials: $q$-integral representation and combinatorial formula”, Compositio Math., 112:2 (1998), 147–182 | DOI | MR | Zbl

[9] Okounkov A., “Binomial formula for Macdonald polynomials and applications”, Math. Res. Lett., 4:4 (1997), 533–553 | DOI | MR | Zbl

[10] Okounkov A., “BC-type interpolation Macdonald polynomials and binomial formula for Koornwinder polynomials”, Transform. Groups, 3:2 (1998), 181–207 | DOI | MR | Zbl

[11] Okounkov A., Combinatorial formula for Macdonald polynomials, Bethe Ansatz, and generic Macdonald polynomials, arXiv: /math.QA/0008094 | MR

[12] Okounkov A., Olshanski G., “Shifted Jack polynomials, binomial formula, and applications”, Math. Res. Lett., 4:1 (1997), 69–78 | DOI | MR | Zbl

[13] Sahi S., “Interpolation, integrality, and a generalization of Macdonald's polynomials”, Internat. Math. Res. Notices, 1996, no. 10, 457–471 | DOI | MR | Zbl

[14] Sahi S., “The binomial formula for nonsymmetric Macdonald polynomials”, Duke Math. J., 94:3 (1998), 465–477 | DOI | MR | Zbl