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A combinatorial formula for non-symmetric Macdonald polynomials

J. Haglund·M. Haiman·N. Loehr
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Abstract

We give a combinatorial formula for the non-symmetric Macdonald polynomials E_μ(x;q,t). The formula generalizes our previous combinatorial interpretation of the integral form symmetric Macdonald polynomials J_μ(x;q,t). We prove the new formula by verifying that it satisfies a recurrence, due to Knop, that characterizes the non-symmetric Macdonald polynomials.

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J. Haglund, M. Haiman, N. Loehr. 2007-02-12. A combinatorial formula for non-symmetric Macdonald polynomials. https://arxiv.org/abs/math/0601693

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