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SIGMA 3 (2007), 065, 11 pages arXiv:0705.0468
https://doi.org/10.3842/SIGMA.2007.065
Contribution to the Vadim Kuznetsov Memorial Issue
The Rahman Polynomials Are Bispectral
F. Alberto Grünbaum
Department of Mathematics, University of California, Berkeley, CA 94720, USA
Received February 01, 2007, in final form April
22, 2007; Published online May 03, 2007
Abstract
In a very recent paper, M. Rahman introduced a remarkable family of polynomials
in two variables as the eigenfunctions of the transition matrix for a nontrivial
Markov chain due to M. Hoare and M. Rahman.
I indicate here that these polynomials are bispectral. This should be just one of the many
remarkable properties enjoyed by these polynomials. For several challenges, including
finding a general proof of some of the facts displayed here the reader should look
at the last section of this paper.
Key words:
bispectral property; multivariable polynomials; rings of commuting difference operators.
pdf (208 kb)
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