A combinatorial formula for non-symmetric Macdonald polynomials

By James Haglund, Mark D. Haiman, Nicholas A. Loehr. 2006

58 citations recorded by the source corpus.

We give a combinatorial formula for the non-symmetric 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 Knop, that characterizes the non-symmetric Macdonald polynomials.

View Paper: https://www.semanticscholar.org/paper/384c62dbaf8e56310f1858b1991466f918315dcb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Martha Yip
2. Arun Ram
3. James Haglund
4. Stephen Griffeth
5. I. Gordon

Citations in the corpus

• A combinatorial formula for Macdonald polynomials (2008, methodology): “These expansions, when applied to the generator of the polynomial representation of the DAHA, give formulas for the Macdonald polynomials which are generalizations, to all root systems, of the formulas obtained by Haglund-Haiman-Loehr [HHL1] [ HHL2 ] in type GLn.”
• A DECOMPOSITION OF SCHUR FUNCTIONS AND AN ANALOGUE OF THE ROBINSON-SCHENSTED-KNUTH ALGORITHM (2006, unknown): “The column diagram of γ is a figure dg ′ (γ) consisting of n cells arranged into columns, as in [3].”