Comparing formulas for type GL n Macdonald polynomials
Copyright policy )Comparing formulas for type GL n Macdonald polynomials
The paper compares (and reproves) the alcove walk and the nonattacking fillings formulas for type GL n Macdonald polynomials which were given in [10], [1] and [18]. The “compression” relating the two formulas in this paper is the same as that of Lenart [13]. We have reformulated it so that it holds without conditions and so that the proofs of the alcove walks formula and the nonattacking fillings formula are parallel. This reformulation highlights the role of the double affine Hecke algebra and Cherednik’s intertwiners. An exposition of the type GL n double affine braid group, double affine Hecke algebra, and all definitions and proofs regarding Macdonald polynomials are provided to make this paper self contained.
- University of Melbourne Australia
Symmetric functions and generalizations, tableaux, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Hecke algebras and their representations, Combinatorial aspects of representation theory, FOS: Mathematics, Mathematics - Combinatorics, Macdonald polynomials, Combinatorics (math.CO), Representation Theory (math.RT), affine Hecke algebras, Mathematics - Representation Theory
Symmetric functions and generalizations, tableaux, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Hecke algebras and their representations, Combinatorial aspects of representation theory, FOS: Mathematics, Mathematics - Combinatorics, Macdonald polynomials, Combinatorics (math.CO), Representation Theory (math.RT), affine Hecke algebras, Mathematics - Representation Theory
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