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Preprints, Working Papers, ... Year : 2024

Factorized $A_2$-Leonard pair

Abstract

The notion of factorized $A_2$-Leonard pair is introduced. It is defined as a rank 2 Leonard pair, with actions in certain bases corresponding to the root system of the Weyl group $A_2$, and with some additional properties. The functions arising as entries of transition matrices are bivariate orthogonal polynomials (of Tratnik type) with bispectral properties. Examples of factorized $A_2$-Leonard pairs are constructed using classical Leonard pairs associated to families of orthogonal polynomials of the ($q$-)Askey scheme. The most general examples are associated to an intricate product of univariate ($q$-)Hahn and dual ($q$-)Hahn polynomials.

Dates and versions

hal-04595412 , version 1 (31-05-2024)

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Cite

Nicolas Crampé, Meri Zaimi. Factorized $A_2$-Leonard pair. 2024. ⟨hal-04595412⟩
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