Inversion of the Pieri formula for Macdonald polynomials

Advances in Mathematics

Volumn 202, Issue 2, 2006, Pages 289-325

  Lassalle, Michel ^a   Schlosser, Michael ^b  

^a CNRS   (France)

^b UNIVERSITY OF VIENNA   (Austria)

Author keywords

Hall Littlewood polynomials; Jack polynomials; Jacobi Trudi expansion; Macdonald polynomials; Matrix inversion; Pieri formula; Schur functions; Symmetric functions

Indexed keywords

EID: 33646121973     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2005.03.009     Document Type: Article

References (25)

1. Bressoud D.M. A matrix inverse. Proc. Amer. Math. Soc. 88 (1983) 446-448
2. G. Gasper, M. Rahman, Basic Hypergeometric Series, Encyclopedia of Mathematics and its Applications, vol. 35, Cambridge University Press, Cambridge, 1990.
3. Hua L.-K. Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains (1963), American Mathematical Society, Providence
4. James A.T. Zonal polynomials of the real positive definite symmetric matrices. Ann. Math. 74 (1961) 456-469
5. Jing N.H., and Józefiak T. A formula for two-row Macdonald functions. Duke Math. J. 67 (1992) 377-385
6. S. Kerov, Generalized Hall-Littlewood Symmetric Functions and Orthogonal Polynomials, vol. 9, Advances in Soviet Mathematics, American Mathematical Society, Providence, RI, 1992, pp. 67-94.
7. Kerov S. Asymptotic Representation Theory of the Symmetric Group and its Applications in Analysis (2003), American Mathematical Society, Providence, RI
8. n unpublished manuscript, 1988, http://remote.science.uva.nl/ ∼thk/recentpapers/dualmacdonald.pdf.
9. Krattenthaler C. Operator methods and Lagrange inversion, a unified approach to Lagrange formulas. Trans. Amer. Math. Soc. 305 (1988) 431-465
10. Krattenthaler C. A new matrix inverse. Proc. Amer. Math. Soc. 124 (1996) 47-59
11. Krattenthaler C., and Schlosser M. A new multidimensional matrix inverse with applications to multiple q-series. Discrete Math. 204 (1999) 249-279
12. Lapointe L., Lascoux A., and Morse J. Determinantal expressions for Macdonald polynomials. Internat. Math. Res. Notes 18 (1998) 957-978
13. A. Lascoux, Symmetric Functions and Combinatorial Operators on Polynomials, CBMS/AMS Lectures Notes, vol. 99, 2003.
14. Lassalle M. Explicitation des polynômes de Jack et de Macdonald en longueur trois. C. R. Acad. Sci. Paris Sér. I Math. 333 (2001) 505-508
15. Lassalle M. Une q - spécialisation pour les fonctions symétriques monomiales. Adv. Math. 162 (2001) 217-242
16. M. Lassalle, A short proof of generalized Jacobi-Trudi expansions for Macdonald polynomials, http://arXiv.org/abs/math.CO/0401032, to appear in Jack, Hall-Littlewood and Macdonald Polynomials, Contemp. Math.
17. Lassalle M., and Schlosser M. An analytic formula for Macdonald polynomials. C. R. Math. Acad. Sci. Paris 337 (2003) 569-574
18. λ ( x ; q, t ): facts and conjectures, unpublished manuscript, 1987.
19. Macdonald I.G. Symmetric Functions and Hall Polynomials. second ed. (1995), Clarendon Press, Oxford
20. Morris A.O. The characters of the group GL ( n ; q ). Math. Z. 81 (1963) 112-123
21. r basic hypergeometric series. Ramanujan J. 1 (1997) 243-274
22. r. Contemp. Math. 254 (2000) 413-432
23. Stanley R.P. Some combinatorial properties of Jack symmetric functions. Adv. Math. 77 (1989) 76-115
24. A.T. Vandermonde, Mémoire sur la Résolution des Équations, Paris, 1771.
25. E. Waring, Miscellanea Analytica, London, 1762.