This paper is a supplement to [5], containing examples, remarks and additional material that could be useful to researchers working with Type Macdonald polynomials. In the course of our comparison of the alcove walk formula and the nonattacking fillings formulas for type Macdonald polynomials we did many examples and significant analysis of the literature. In the preparation of [5] it seemed sensible to produce a document with focus and this material was removed. This is paper resurrects and organizes that material, in hopes that others may also find it useful.
Accepted:
Revised after acceptance:
Published online:
Keywords: Macdonald polynomials, affine Hecke algebras, tableaux
Guo, Weiying 1; Ram, Arun 2
@article{ALCO_2022__5_5_885_0, author = {Guo, Weiying and Ram, Arun}, title = {Comparing formulas for type $GL_n$ {Macdonald} polynomials {\textendash} {Supplement}}, journal = {Algebraic Combinatorics}, pages = {885--923}, publisher = {The Combinatorics Consortium}, volume = {5}, number = {5}, year = {2022}, doi = {10.5802/alco.228}, language = {en}, url = {https://alco.centre-mersenne.org/articles/10.5802/alco.228/} }
TY - JOUR AU - Guo, Weiying AU - Ram, Arun TI - Comparing formulas for type $GL_n$ Macdonald polynomials – Supplement JO - Algebraic Combinatorics PY - 2022 SP - 885 EP - 923 VL - 5 IS - 5 PB - The Combinatorics Consortium UR - https://alco.centre-mersenne.org/articles/10.5802/alco.228/ DO - 10.5802/alco.228 LA - en ID - ALCO_2022__5_5_885_0 ER -
%0 Journal Article %A Guo, Weiying %A Ram, Arun %T Comparing formulas for type $GL_n$ Macdonald polynomials – Supplement %J Algebraic Combinatorics %D 2022 %P 885-923 %V 5 %N 5 %I The Combinatorics Consortium %U https://alco.centre-mersenne.org/articles/10.5802/alco.228/ %R 10.5802/alco.228 %G en %F ALCO_2022__5_5_885_0
Guo, Weiying; Ram, Arun. Comparing formulas for type $GL_n$ Macdonald polynomials – Supplement. Algebraic Combinatorics, Volume 5 (2022) no. 5, pp. 885-923. doi : 10.5802/alco.228. https://alco.centre-mersenne.org/articles/10.5802/alco.228/
[1] Nonsymmetric Macdonald polynomials via integrable vertex models (2019) | arXiv
[2] Matrix product formula for Macdonald polynomials, J. Phys. A, Volume 48 (2015) no. 38, p. 384001, 25 pages | DOI | MR | Zbl
[3] Matrix product and sum rule for Macdonald polynomials, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (Discrete Math. Theor. Comput. Sci. Proc., BC), Assoc. Discrete Math. Theor. Comput. Sci., Nancy, [2016] ©2016, pp. 311-321 | MR | Zbl
[4] From multiline queues to Macdonald polynomials via the exclusion process, Sém. Lothar. Combin., Volume 82B (2020), p. Art. 97, 12 pages | MR | Zbl
[5] Comparing formulas for type Macdonald polynomials, Algebr. Comb., Volume 5 (2022) no. 5, pp. 849-883 | arXiv
[6] A combinatorial formula for nonsymmetric Macdonald polynomials, Amer. J. Math., Volume 130 (2008) no. 2, pp. 359-383 | DOI | MR | Zbl
[7] The ,-Catalan numbers and the space of diagonal harmonics, University Lecture Series, 41, American Mathematical Society, Providence, RI, 2008, viii+167 pages (With an appendix on the combinatorics of Macdonald polynomials) | DOI | MR
[8] The quantum Knizhnik-Zamolodchikov equation and non-symmetric Macdonald polynomials, Funkcial. Ekvac., Volume 50 (2007) no. 3, pp. 491-509 | DOI | MR | Zbl
[9] On combinatorial formulas for Macdonald polynomials, Adv. Math., Volume 220 (2009) no. 1, pp. 324-340 | DOI | MR | Zbl
[10] Symmetric functions and Hall polynomials. With contributions by A. Zelevinsky, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1995, x+475 pages | MR
[11] Affine Hecke algebras and orthogonal polynomials, Astérisque (1996) no. 237, pp. Exp. No. 797, 4, 189-207 (Séminaire Bourbaki, Vol. 1994/95) | Numdam | MR | Zbl
[12] Affine Hecke algebras and orthogonal polynomials, Cambridge Tracts in Mathematics, 157, Cambridge University Press, Cambridge, 2003, x+175 pages | DOI | MR
[13] Lectures on Chevalley groups, Yale University New Haven, 1967 (Notes prepared by John Faulkner and Robert Wilson. Revised and corrected edition of the 1968 original) | MR
Cited by Sources: