A combinatorial formula for nonsymmetric Macdonald polynomials. (English) Zbl 1246.05162

Haglund, J.; Haiman, M.; Loehr, N.

Am. J. Math. 130, No. 2, 359-383 (2008).

We give a combinatorial formula for the nonsymmetric Macdonald polynomials \(E_{\mu}(x; q, t)\). The formula generalizes our previous combinatorial interpretation of the integral form symmetric Macdonald polynomials \(J_{\mu}(x; q, t)\). We prove the new formula by verifying that it satisfies a recurrence, due to F. Knop and S. Sahi [Invent. Math. 128, No. 1, 9–22 (1997; Zbl 0870.05076)], that characterizes the nonsymmetric Macdonald polynomials.

MSC:

05E05	Symmetric functions and generalizations
33D52	Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)

Keywords:

integral form symmetric Macdonald polynomials

Citations:

Zbl 0870.05076