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arXiv · 0802.1454

Macdonald polynomials at $t=q^k$

Jean-Gabriel Luque
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Abstract

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

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Jean-Gabriel Luque. 2008-02-11. Macdonald polynomials at $t=q^k$. https://doi.org/10.1016/j.jalgebra.2009.11.012

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