Macdonald polynomials at $t=q^k$

Details Macdonald polynomials at $t=q^k$ Macdonald polynomials at $t=q^k$

2008-02-11

arxiv.org/abs/0802.1454v1

Journal of Algebra 324 (2010) 36-50

Mathematics

Combinatorics

19pp; Journal of Algebra (2009) In Press

Scientific paper

10.1016/j.jalgebra.2009.11.012

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
$P_\lambda(\frac{1-q}{1-q^k}\X;q,q^k)$. As a consequence, we describe an
operator whose eigenvalues characterize the polynomials $P_\lambda(\X;q,q^k)$.

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