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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-09-01
|
| Series: | Nuclear Physics B |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321325002925 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849226979433250816 |
|---|---|
| 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. |
| format | Article |
| id | doaj-art-05f829d6d9b943d6a3bba53d29ad63f9 |
| institution | Kabale University |
| issn | 0550-3213 |
| language | English |
| publishDate | 2025-09-01 |
| publisher | Elsevier |
| record_format | Article |
| 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 |
| work_keys_str_mv | AT nicolascrampe changeofbasisfortridiagonalpairsoftypeii AT juliengaboriaud changeofbasisfortridiagonalpairsoftypeii AT satoshitsujimoto changeofbasisfortridiagonalpairsoftypeii |