Geodesic
A bijective proof of a factorization formula for Macdonald polynomials at roots of unity
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) (2008).

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We give a combinatorial proof of the factorization formula of modified Macdonald polynomials $\widetilde{H}_{\lambda} (X;q,t)$ when $t$ is specialized at a primitive root of unity. Our proof is restricted to the special case where $\lambda$ is a two columns partition. We mainly use the combinatorial interpretation of Haiman, Haglund and Loehr giving the expansion of $\widetilde{H}_{\lambda} (X;q,t)$ on the monomial basis. 
@article{DMTCS_2008_special_255_a1,
     author = {Descouens, F. and Morita, H. and Numata, Y.},
     title = {A bijective proof of a factorization formula for {Macdonald} polynomials at roots of unity},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)},
     year = {2008},
     doi = {10.46298/dmtcs.3593},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3593/}
}
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Descouens, F.; Morita, H.; Numata, Y. A bijective proof of a factorization formula for Macdonald polynomials at roots of unity. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) (2008). doi : 10.46298/dmtcs.3593. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3593/

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