Meta algebras and biorthogonal rational functions: the $q$-Hahn case
Representation Theory
2024-10-22 v1
Abstract
A unified algebraic interpretation of both finite families of orthogonal polynomials and biorthogonal rational functions of -Hahn type is provided. The approach relies on the meta -Hahn algebra and its finite-dimensional bidiagonal representations. The functions of -Hahn type are identified as overlaps (up to global factors) between bases solving ordinary or generalized eigenvalue problems in the representation of the meta -Hahn algebra. Moreover, (bi)orthogonality relations, recurrence relations, difference equations and some contiguity relations satisfied by these functions are recovered algebraically using the actions of the generators of the meta -Hahn algebra on various bases.
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Cite
@article{arxiv.2410.14856,
title = {Meta algebras and biorthogonal rational functions: the $q$-Hahn case},
author = {Pierre-Antoine Bernard and Abderahmane Bouziane and Samuel Pellerin and Simone Têtu and Satoshi Tsujimoto and Luc Vinet and Meri Zaimi and Alexei Zhedanov},
journal= {arXiv preprint arXiv:2410.14856},
year = {2024}
}
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27 pages