A Littlewood-Richardson rule for Macdonald polynomials

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6 Scopus citations

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.

Original languageEnglish
Pages (from-to)1259-1290
Number of pages32
JournalMathematische Zeitschrift
Volume272
Issue number3-4
DOIs
StatePublished - Dec 2012

Keywords

  • Affine Hecke algebra
  • Combinatorial formula
  • Macdonald polynomials
  • Symmetric functions

ASJC Scopus subject areas

  • Mathematics (all)

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