A combinatorial formula for non-symmetric Macdonald polynomials

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.

22 pages, to appear in Amer. J. Math

References in corpus (4)

• A recursion and a combinatorial formula for Jack polynomials
• Difference equations and symmetric polynomials defined by their zeros
• Macdonald's Evaluation Conjectures and Difference Fourier Transform
• Integrality of two variable Kostka functions

Cited by in corpus (13)

• Combinatorial rules for three bases of polynomials
• Extremal part of the PBW-filtration and E-polynomials
• Newton Polytopes in Algebraic Combinatorics
• Demazure crystals for Kohnert polynomials
• An analogue of the Robinson-Schensted-Knuth correspondence and non-symmetric Cauchy kernels for truncated staircases
• Symplectic keys and Demazure atoms in type C
• Comparing formulas for type $G{L}_n$ Macdonald polynomials
• Comparing formulas for type $G{L}_n$ Macdonald polynomials: Supplement
• Demazure crystals, Kirillov-Reshetikhin crystals, and the energy function
• Hall-Littlewood symmetric functions via Yamanouchi toppling game
• Relating three combinatorial formulas for type $A$ Whittaker functions
• Skew row-strict quasisymmetric Schur functions
• A Littlewood-Richardson rule for Macdonald polynomials