HAL: hal-00250315, version 1

arXiv: 0802.1454

DOI: 10.1016/j.jalgebra.2009.11.012

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Journal of Algebra 324 (2010) 36-50

Macdonald polynomials at $t=q^k$

Jean-Gabriel Luque 1

(2010)

We investigate the homogeneous symmetric Macdonald polynomials $P_\lambda(\X;q,t)$ for the specialization $t=q^k$. We show an identity relying the polynomials $P_\lambda(\X;q,q^k)$ and $P_\lambda\left(\frac{1-q}{1-q^k}\X;q,q^k\right)$. As a consequence, we describe an operator whose eigenvalues characterize the polynomials $P_\lambda(\X;q,q^k)$.

1:	Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS)
	Institut National des Sciences Appliquées (INSA) - Rouen – Université du Havre – Université de Rouen : EA4108

Subject

:

Mathematics/Combinatorics

Keyword(s): Macdonald polynomials – q-discriminant – Cherednik operators – Hecke algebra

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From: Jean-Gabriel Luque <>

Submitted on: Monday, 11 February 2008 16:03:34

Updated on: Thursday, 13 May 2010 07:34:30