A Littlewood-Richardson rule for Macdonald polynomials

2010/10/04 by Martha Yip, Yip, Martha
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1010.0722

openalex publication_date 2010/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Macdonald polynomials are orthogonal polynomials associated to root systems, and in the type A case, the symmetric kind is a common generalization of Schur functions, Macdonald spherical functions, and Jack polynomials. We use the combinatorics of alcove walks to calculate products of monomials and intertwining operators of the double affine Hecke algebra. From this, we obtain a product formula for Macdonald polynomials of general type.

Citations

• One-skeleton galleries, the path model and a generalization of Macdonald's formula for Hall-Littlewood polynomials

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