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A Littlewood–Richardson rule for Macdonald polynomials

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Abstract

Macdonald polynomials are orthogonal polynomials associated to root systems, and in the type A case, the symmetric Macdonald polynomials are 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 Lie type.

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  1. Department of Mathematics, University of Pennsylvania, Philadelphia, PA, 19104, USA

    Martha Yip

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  1. Martha Yip
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Correspondence to Martha Yip.

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Yip, M. A Littlewood–Richardson rule for Macdonald polynomials. Math. Z. 272, 1259–1290 (2012). https://doi.org/10.1007/s00209-012-0986-z

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  • DOI: https://doi.org/10.1007/s00209-012-0986-z

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