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A short proof of the integrality of the Macdonald $(q,t)$-Kostka coefficients
Luc Lapointe and Luc Vinet
Source: Duke Math. J. Volume 91, Number 1
(1998), 205-214.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077231894
Mathematical Reviews number (MathSciNet): MR1487984
Zentralblatt MATH identifier: 0939.05081
Digital Object Identifier: doi:10.1215/S0012-7094-98-09109-8
References
[1] A. M. Garsia and J. Remmel, Plethystic formulas and positivity for $q,t$-Kostka coefficients, preprint.
Mathematical Reviews (MathSciNet): MR1627327
[2] A. M. Garsia and G. Tesler, Plethystic formulas for Macdonald $q,t$-Kostka coefficients, Adv. Math. 123 (1996), no. 2, 144–222.
Mathematical Reviews (MathSciNet): MR99j:05189e
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Digital Object Identifier: doi:10.1006/aima.1996.0071
[3] G. Gasper and M. Rahman, Basic hypergeometric series, Encyclopedia of Mathematics and its Applications, vol. 35, Cambridge University Press, Cambridge, 1990.
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Zentralblatt MATH: 0695.33001
[4] A. Kirillov and M. Noumi, Affine Hecke algebras and raising operators for Macdonald polynomials, Duke Math. J., to appear.
Mathematical Reviews (MathSciNet): MR1620075
Zentralblatt MATH: 0939.05090
Digital Object Identifier: doi:10.1215/S0012-7094-98-09301-2
Project Euclid: euclid.dmj/1077230635
[5] A. Kirillov and M. Noumi, $q$-difference raising operators for Macdonald polynomials and the integrality of transitions coefficients, preprint.
Mathematical Reviews (MathSciNet): MR1726838
Zentralblatt MATH: 0947.33015
[6] F. Knop, Integrality of two variable Kostka functions, J. Reine Angew. Math. 482 (1997), 177–189.
Mathematical Reviews (MathSciNet): MR99j:05189c
Zentralblatt MATH: 0876.05098
Digital Object Identifier: doi:10.1515/crll.1997.482.177
[7] F. Knop, Symmetric and non-symmetric quantum Capelli polynomials, preprint.
Mathematical Reviews (MathSciNet): MR1456318
Zentralblatt MATH: 0954.05049
[8] L. Lapointe and L. Vinet, Creation operators for the Macdonald and Jack polynomials, Lett. Math. Phys. 40 (1997), no. 3, 269–286.
Mathematical Reviews (MathSciNet): MR99f:05130
Zentralblatt MATH: 0882.33010
Digital Object Identifier: doi:10.1023/A:1007332315944
[9] L. Lapointe and L. Vinet, Exact operator solution of the Calogero-Sutherland model, Comm. Math. Phys. 178 (1996), no. 2, 425–452.
Mathematical Reviews (MathSciNet): MR97c:81217
Zentralblatt MATH: 0859.35103
Digital Object Identifier: doi:10.1007/BF02099456
Project Euclid: euclid.cmp/1104286659
[10] L. Lapointe and L. Vinet, A Rodrigues formula for the Jack polynomials and the Macdonald-Stanley conjecture, Internat. Math. Res. Notices (1995), no. 9, 419–424.
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Digital Object Identifier: doi:10.1155/S1073792895000298
[11] L. Lapointe and L. Vinet, Rodrigues formula for the Macdonald polynomials, to appear in Adv. Math.
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Digital Object Identifier: doi:10.1006/aima.1997.1662
[12] L. Lapointe and L. Vinet, Creation operators for the Calogero-Sutherland model, in preparation.
[13] I. G. Macdonald, Symmetric functions and Hall polynomials, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, 1995.
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[14] S. Sahi, Interpolation, integrality, and a generalization of Macdonald's polynomials, Internat. Math. Res. Notices (1996), no. 10, 457–471.
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Digital Object Identifier: doi:10.1155/S107379289600030X
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