A conjecture about raising operators for Macdonald polynomials. (English) Zbl 1079.33015
The author presents a conjecture giving Macdonald polynomials as a hypergeometric-type series in terms of raising operators. He shows that this conjecture agrees with Jing and Jozefiak’s expression in the two-row case, and with Lassalle and Schlosser’s formula in the three-row case.
Reviewer: Hari M. Srivastava (Victoria)
MSC:
| 33D52 | Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) |
| 33D67 | Basic hypergeometric functions associated with root systems |
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
References:
| [2] | Macdonald, I. G. Symmetric Functions and Hall Polynomials, 2nd edn. Oxford University Press, 1995. · Zbl 0824.05059 |
| [5] | Lassalle, M. and Schlosser, M.: Inversion of the Pieri formula for Macdonald polynomials, math.CO/0402127, to appear in Adv. Math. · Zbl 1106.33015 |
| [6] | Lassalle, M.: A short proof of generalized Jacobi-Trudi expansions for Macdonald polynomials, math.CO/0401032. · Zbl 1133.05099 |
| [7] | Shiraishi, J.: A Commutative Family of Integral Transformations and Basic Hypergeometric Series. I. Eigenfunctions, math.QA/0501251. · Zbl 1103.33011 |
| [8] | Shiraishi, J.: A Commutative Family of Integral Transformations and Basic Hypergeometric Series. II. Eigenfunctions and Quasi-Eigenfunctions, math.QA/0502228. |
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