F. Descouens ; H. Morita ; Y. Numata - A bijective proof of a factorization formula for Macdonald polynomials at roots of unity

dmtcs:3593 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) - https://doi.org/10.46298/dmtcs.3593
A bijective proof of a factorization formula for Macdonald polynomials at roots of unityArticle

Authors: F. Descouens 1,2; H. Morita 3; Y. Numata 4

  • 1 Fields Institute for Research In Mathematical Sciences
  • 2 Department of Mathematics and Statistics [Toronto]
  • 3 Oyama National College of Technology
  • 4 Department of Mathematics [Sapporo]

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.


Volume: DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
Section: Proceedings
Published on: January 1, 2008
Imported on: May 10, 2017
Keywords: Macdonald polynomials,roots of unity,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

1 Document citing this article

Consultation statistics

This page has been seen 182 times.
This article's PDF has been downloaded 172 times.