A combinatorial formula for Macdonald polynomials

By Arun Ram, Martha Yip. 2008

190 citations recorded by the source corpus.

Abstract In this paper we use the combinatorics of alcove walks to give uniform combinatorial formulas for Macdonald polynomials for all Lie types. These formulas resemble the formulas of Haglund, Haiman and Loehr for Macdonald polynomials of type GL n . At q = 0 these formulas specialize to the formula of Schwer for the Macdonald spherical function in terms of positively folded alcove walks and at q = t = 0 these formulas specialize to the formula for the Weyl character in terms of the Littelmann path model (in the positively folded gallery form of Gaussent and Littelmann).

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/39c5a8d842f46d3bd2de2003b7d58b73a15e6e06

How researchers see this paper

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

In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

A DECOMPOSITION OF SCHUR FUNCTIONS AND AN ANALOGUE OF THE ROBINSON-SCHENSTED-KNUTH ALGORITHM (2006, unknown): “This diagram, called the Young (or Ferrers) diagram, is drawn in the first quadrant, French style, as in [1].”
Crystal structure on rigged configurations (2005, background): “The Lascoux–Leclerc–Thibon (LLT) polynomials [31, 32] have recently made their debut in the theory of Macdonald polynomials in the seminal paper by Haiman, Haglund, Loehr [11].”
A Combinatorial Formula for Nonsymmetric Macdonald Polynomials (2008, methodology): “In a previous paper [6], we gave a combinatorial formula for Macdonald’s symmetric functions (for root systems of type A).”