ALGEBRAIC COMBINATORICS

Comparing formulas for type $G{L}_{n}$ Macdonald polynomials
Algebraic Combinatorics, Volume 5 (2022) no. 5, pp. 849-883.

The paper compares (and reproves) the alcove walk and the nonattacking fillings formulas for type $G{L}_{n}$ 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 $G{L}_{n}$ double affine braid group, double affine Hecke algebra, and all definitions and proofs regarding Macdonald polynomials are provided to make this paper self contained.

Revised:
Accepted:
Published online:
DOI: 10.5802/alco.227
Classification: 05E05,  33D52
Keywords: Macdonald polynomials, affine Hecke algebras, tableaux
Guo, Weiying 1; Ram, Arun 1

1 University of Melbourne School of Mathematics and statistics Parkville Vic 3010. Melbourne
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Guo, Weiying; Ram, Arun. Comparing formulas for type $GL_n$ Macdonald polynomials. Algebraic Combinatorics, Volume 5 (2022) no. 5, pp. 849-883. doi : 10.5802/alco.227. https://alco.centre-mersenne.org/articles/10.5802/alco.227/

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