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A reproducing kernel for nonsymmetric Macdonald polynomials
Katsuhisa Mimachi and Masatoshi Noumi
Source: Duke Math. J. Volume 91, Number 3
(1998), 621-634.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077232261
Mathematical Reviews number (MathSciNet): MR1604183
Zentralblatt MATH identifier: 0947.33014
Digital Object Identifier: doi:10.1215/S0012-7094-98-09124-4
References
[C1] I. Cherednik, Double affine Hecke algebras and Macdonald's conjectures, Ann. of Math. (2) 141 (1995), no. 1, 191–216.
Mathematical Reviews (MathSciNet): MR96m:33010
Zentralblatt MATH: 0822.33008
Digital Object Identifier: doi:10.2307/2118632
JSTOR: links.jstor.org
[C2] I. Cherednik, Nonsymmetric Macdonald polynomials, Internat. Math. Res. Notices (1995), no. 10, 483–515.
Mathematical Reviews (MathSciNet): MR97f:33032
Zentralblatt MATH: 0886.05121
Digital Object Identifier: doi:10.1155/S1073792895000341
[KN] A. N. Kirillov and M. Noumi, Affine Hecke algebras and raising operators for Macdonald polynomials, to appear in Duke Math. J.
Mathematical Reviews (MathSciNet): MR1620075
Zentralblatt MATH: 0939.05090
Digital Object Identifier: doi:10.1215/S0012-7094-98-09301-2
Project Euclid: euclid.dmj/1077230635
[KS] F. Knop and S. Sahi, A recursion and a combinatorial formula for Jack polynomials, Invent. Math. 128 (1997), no. 1, 9–22.
Mathematical Reviews (MathSciNet): MR98k:33040
Zentralblatt MATH: 0870.05076
Digital Object Identifier: doi:10.1007/s002220050134
[Ma1] I. G. Macdonald, Affine Hecke algebras and orthogonal polynomials, Astérisque (1996), no. 237, Exp. No. 797, 4, 189–207, in Séminaire Bourbaki, Vol. 1994/95.
Mathematical Reviews (MathSciNet): MR99f:33024
Zentralblatt MATH: 0883.33008
[Ma2] I. G. Macdonald, Symmetric functions and Hall polynomials, 2nd ed. ed., Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, 1995.
Mathematical Reviews (MathSciNet): MR96h:05207
Zentralblatt MATH: 0824.05059
[Mi1] K. Mimachi, A solution to quantum Knizhnik-Zamolodchikov equations and its application to eigenvalue problems of the Macdonald type, Duke Math. J. 85 (1996), no. 3, 635–658.
Mathematical Reviews (MathSciNet): MR98f:17019
Zentralblatt MATH: 0889.17009
Digital Object Identifier: doi:10.1215/S0012-7094-96-08524-5
Project Euclid: euclid.dmj/1077243445
[Mi2] K. Mimachi, A new derivation of the inner product formula for the Macdonald symmetric polynomials, to appear in Compositio Math.
Mathematical Reviews (MathSciNet): MR1639175
Zentralblatt MATH: 0932.33028
Digital Object Identifier: doi:10.1023/A:1000356515121
[MN] K. Mimachi and M. Noumi, Representations of a Hecke algebra on a family of rational functions, preprint, 1997.
[O] E. Opdam, Harmonic analysis for certain representations of graded Hecke algebras, Acta Math. 175 (1995), no. 1, 75–121.
Mathematical Reviews (MathSciNet): MR98f:33025
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Digital Object Identifier: doi:10.1007/BF02392487
[S] S. Sahi, A new scalar product for nonsymmetric Jack polynomials, Internat. Math. Res. Notices (1996), no. 20, 997–1004.
Mathematical Reviews (MathSciNet): MR98g:05154
Zentralblatt MATH: 0885.33006
Digital Object Identifier: doi:10.1155/S107379289600061X
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