# Macdonald polynomials at $t=q^k$

Abstract : We investigate the homogeneous symmetric Macdonald polynomials $P_{\lambda} (\mathbb{X} ;q,t)$ for the specialization $t=q^k$. We show an identity relying the polynomials $P_{\lambda} (\mathbb{X} ;q,q^k)$ and $P_{\lambda} (\frac{1-q}{1-q^k}\mathbb{X} ;q,q^k)$. As a consequence, we describe an operator whose eigenvalues characterize the polynomials $P_{\lambda} (\mathbb{X} ;q,q^k)$.
Keywords :
Document type :
Conference papers
Domain :

Cited literature [13 references]

https://hal.inria.fr/hal-01185379
Contributor : Coordination Episciences Iam <>
Submitted on : Thursday, August 20, 2015 - 11:06:40 AM
Last modification on : Wednesday, August 21, 2019 - 10:30:06 AM
Long-term archiving on: : Wednesday, April 26, 2017 - 10:08:14 AM

### File

dmAK0149.pdf
Publisher files allowed on an open archive

### Identifiers

• HAL Id : hal-01185379, version 1

### Citation

Jean-Gabriel Luque. Macdonald polynomials at $t=q^k$. 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. pp.585-596. ⟨hal-01185379⟩

Record views