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