A Littlewood-Richardson rule for Macdonald polynomials

Details A Littlewood-Richardson rule for Macdonald polynomials A Littlewood-Richardson rule for Macdonald polynomials

2010-10-04

arxiv.org/abs/1010.0722v1

Mathematics

Combinatorics

43 pages

Scientific paper

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.

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