On combinatorial formulas for Macdonald polynomials

• Autores: Cristian Lenart
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 220, Nº 1, 2009, págs. 324-340
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • A recent breakthrough in the theory of (type A) Macdonald polynomials is due to Haglund, Haiman and Loehr, who exhibited a combinatorial formula for these polynomials in terms of a pair of statistics on fillings of Young diagrams. Ram and Yip gave a formula for the Macdonald polynomials of arbitrary type in terms of so-called alcove walks; these originate in the work of Gaussent�Littelmann and of the author with Postnikov on discrete counterparts to the Littelmann path model. In this paper, we relate the above developments, by explaining how the Ram�Yip formula compresses to a new formula, which is similar to the Haglund�Haiman�Loehr one but contains considerably fewer terms