We give the explicit analytic development of any Jack or Macdonald polynomial in terms of elementary (resp. modified complete) symmetric functions. These two developments are obtained by inverting the Pieri formula.
Nous donnons le développement analytique explicite de tout polynôme de Jack ou de Macdonald sur les fonctions symétriques élémentaires (resp. complètes modifiées). Nous obtenons ces deux développements par inversion de la formule de Pieri.
Accepted:
Published online:
Michel Lassalle 1; Michael Schlosser 2
@article{CRMATH_2003__337_9_569_0, author = {Michel Lassalle and Michael Schlosser}, title = {An analytic formula for {Macdonald} polynomials}, journal = {Comptes Rendus. Math\'ematique}, pages = {569--574}, publisher = {Elsevier}, volume = {337}, number = {9}, year = {2003}, doi = {10.1016/j.crma.2003.09.020}, language = {en}, }
Michel Lassalle; Michael Schlosser. An analytic formula for Macdonald polynomials. Comptes Rendus. Mathématique, Volume 337 (2003) no. 9, pp. 569-574. doi : 10.1016/j.crma.2003.09.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.09.020/
[1] Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains, American Mathematical Society, Providence, 1963
[2] A formula for two-row Macdonald functions, Duke Math. J., Volume 67 (1992), pp. 377-385
[3] Operator methods and Lagrange inversion, a unified approach to Lagrange formulas, Trans. Amer. Math. Soc., Volume 305 (1988), pp. 431-465
[4] A new matrix inverse, Proc. Amer. Math. Soc., Volume 124 (1996), pp. 47-59
[5] Determinantal expressions for Macdonald polynomials, Int. Math. Res. Not., Volume 18 (1998), pp. 957-978
[6] Explicitation des polynômes de Jack et de Macdonald en longueur trois, C. R. Acad. Sci. Paris, Sér. I Math., Volume 333 (2001), pp. 505-508
[7] Une q-spécialisation pour les fonctions symétriques monomiales, Adv. Math., Volume 162 (2001), pp. 217-242
[8] Symmetric Functions and Hall Polynomials, Clarendon Press, Oxford, 1995
[9] Multidimensional matrix inversions and Ar and Dr basic hypergeometric series, Ramanujan J., Volume 1 (1997), pp. 243-274
Cited by Sources:
Comments - Policy