Change of basis for tridiagonal pairs of type II

This paper is on the topic of tridiagonal pairs of type II. These involve two linear transformations A and A⋆. We define two bases. In the first one, A acts as a diagonal matrix while A⋆ acts as a block tridiagonal matrix, and in the second one, A acts as a block tridiagonal matrix while A⋆ acts as...

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Main Authors: Nicolas Crampé, Julien Gaboriaud, Satoshi Tsujimoto
Format: Article
Language:English
Published: Elsevier 2025-09-01
Series:Nuclear Physics B
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Online Access:http://www.sciencedirect.com/science/article/pii/S0550321325002925
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author Nicolas Crampé
Julien Gaboriaud
Satoshi Tsujimoto
author_facet Nicolas Crampé
Julien Gaboriaud
Satoshi Tsujimoto
author_sort Nicolas Crampé
collection DOAJ
description This paper is on the topic of tridiagonal pairs of type II. These involve two linear transformations A and A⋆. We define two bases. In the first one, A acts as a diagonal matrix while A⋆ acts as a block tridiagonal matrix, and in the second one, A acts as a block tridiagonal matrix while A⋆ acts as a diagonal matrix. We obtain the change of basis coefficients between these two bases. The coefficients are special functions that are written as a nested product of polynomials that resemble Racah polynomials but involve shift operators in their expression.
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institution Kabale University
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publishDate 2025-09-01
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series Nuclear Physics B
spelling doaj-art-05f829d6d9b943d6a3bba53d29ad63f92025-08-24T05:11:28ZengElsevierNuclear Physics B0550-32132025-09-01101811708310.1016/j.nuclphysb.2025.117083Change of basis for tridiagonal pairs of type IINicolas Crampé0Julien Gaboriaud1Satoshi Tsujimoto2Institut Denis-Poisson CNRS/UMR 7013 - Université de Tours - Université d'Orléans, Parc de Grandmont, 37200 Tours, France; Laboratoire d'Annecy-le-Vieux de Physique Théorique LAPTh, Université Savoie Mont Blanc, CNRS, F-74000 Annecy, France; Corresponding author.Graduate School of Informatics, Kyoto University, Sakyo-ku, Kyoto, 606-8501, JapanGraduate School of Informatics, Kyoto University, Sakyo-ku, Kyoto, 606-8501, JapanThis paper is on the topic of tridiagonal pairs of type II. These involve two linear transformations A and A⋆. We define two bases. In the first one, A acts as a diagonal matrix while A⋆ acts as a block tridiagonal matrix, and in the second one, A acts as a block tridiagonal matrix while A⋆ acts as a diagonal matrix. We obtain the change of basis coefficients between these two bases. The coefficients are special functions that are written as a nested product of polynomials that resemble Racah polynomials but involve shift operators in their expression.http://www.sciencedirect.com/science/article/pii/S0550321325002925Tridiagonal pairsLeonard pairsOrthogonal polynomialsMultivariable special functions
spellingShingle Nicolas Crampé
Julien Gaboriaud
Satoshi Tsujimoto
Change of basis for tridiagonal pairs of type II
Nuclear Physics B
Tridiagonal pairs
Leonard pairs
Orthogonal polynomials
Multivariable special functions
title Change of basis for tridiagonal pairs of type II
title_full Change of basis for tridiagonal pairs of type II
title_fullStr Change of basis for tridiagonal pairs of type II
title_full_unstemmed Change of basis for tridiagonal pairs of type II
title_short Change of basis for tridiagonal pairs of type II
title_sort change of basis for tridiagonal pairs of type ii
topic Tridiagonal pairs
Leonard pairs
Orthogonal polynomials
Multivariable special functions
url http://www.sciencedirect.com/science/article/pii/S0550321325002925
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AT juliengaboriaud changeofbasisfortridiagonalpairsoftypeii
AT satoshitsujimoto changeofbasisfortridiagonalpairsoftypeii