Quelques valeurs prises par les polynômes de Macdonald décalés

Michel Lassalle

Annales de l'institut Fourier (1999)

  • Volume: 49, Issue: 2, page 543-561
  • ISSN: 0373-0956

Abstract

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We give explicit expressions for some generalized binomial coefficients associated with Macdonald polynomials, i.e., the value at some special points of shifted Macdonald polynomials. These expressions are obtained in terms of q -basic hypergeometric series.

How to cite

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Lassalle, Michel. "Quelques valeurs prises par les polynômes de Macdonald décalés." Annales de l'institut Fourier 49.2 (1999): 543-561. <http://eudml.org/doc/75346>.

@article{Lassalle1999,
abstract = {Nous explicitons la valeur de certains des coefficients binomiaux généralisés associés aux polynômes de Macdonald, c’est-à-dire la valeur en certains points particuliers des polynômes de Macdonald décalés. Ces expressions font intervenir les fonctions hypergéométriques de base $q$.},
author = {Lassalle, Michel},
journal = {Annales de l'institut Fourier},
keywords = {(Shifted) Macdonald polynomials; generalized binomial formula; generalized binomial coefficients; basic hypergeometric functions},
language = {fre},
number = {2},
pages = {543-561},
publisher = {Association des Annales de l'Institut Fourier},
title = {Quelques valeurs prises par les polynômes de Macdonald décalés},
url = {http://eudml.org/doc/75346},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Lassalle, Michel
TI - Quelques valeurs prises par les polynômes de Macdonald décalés
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 2
SP - 543
EP - 561
AB - Nous explicitons la valeur de certains des coefficients binomiaux généralisés associés aux polynômes de Macdonald, c’est-à-dire la valeur en certains points particuliers des polynômes de Macdonald décalés. Ces expressions font intervenir les fonctions hypergéométriques de base $q$.
LA - fre
KW - (Shifted) Macdonald polynomials; generalized binomial formula; generalized binomial coefficients; basic hypergeometric functions
UR - http://eudml.org/doc/75346
ER -

References

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  2. [2] F. KNOP, Symmetric and non-symmetric quantum Capelli polynomials, to appear. Zbl0954.05049
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  6. [6] M. LASSALLE, Some combinatorial conjectures for shifted Jack polynomials, Ann. Combinatorics, 2 (1998), 145-163. Zbl0933.33014
  7. [7] I. G. MACDONALD, Symmetric functions and Hall polynomials, second edition, Clarendon Press, Oxford, 1995. Zbl0824.05059
  8. [8] A. OKOUNKOV, (Shifted) Macdonald polynomials: q-integral representation and combinatorial formula, Compositio Math., 112 (1998), 147-182. Zbl0897.05085
  9. [9] A. OKOUNKOV, Binomial formula for Macdonald polynomials and applications, Math. Res. Lett., 4 (1997), 533-553. Zbl0911.33012
  10. [10] A. OKOUNKOV, G. OLSHANSKI, Shifted Jack polynomials, binomial formula and applications, Math. Res. Lett., 4 (1997), 69-78. Zbl0995.33013
  11. [11] A. OKOUNKOV, G. OLSHANSKI, Shifted Schur functions, St. Petersburg Math. J., 9 (1998). 
  12. [12] S. SAHI, Interpolation, integrality, and a generalization of Macdonald's polynomials, Internat. Math. Res. Notices, 10 (1996), 457-471. Zbl0861.05063MR99j:05189b

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