Algebraic interpretation of discrete families of matrix valued orthogonal polynomials
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911628560171008 |
|---|---|
| author | Labriet, Quentin Morey, Lucia Vinet, Luc |
| author_facet | Labriet, Quentin Morey, Lucia Vinet, Luc |
| contents | An algebraic interpretation of matrix-valued orthogonal polynomials (MVOPs) is provided. The construction is based on representations of a ($q$-deformed) Lie algebra $\mathfrak{g}$ into the algebra $\operatorname{End}_{M_n(\mathbb{C})}(M)$ of $M_n(\mathbb{C})$-linear maps over a $M_n(\mathbb{C})$-module $M$. Cases corresponding to the Lie algebras $\mathfrak{su}(2)$ and $\mathfrak{su}(1, 1)$ as well as to the $q$-deformed algebra $\mathfrak{so}_q(3)$ at $q$ a root of unity are presented; they lead to matrix analogs of the Krawtchouk, Meixner and discrete Chebyshev polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25948 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algebraic interpretation of discrete families of matrix valued orthogonal polynomials Labriet, Quentin Morey, Lucia Vinet, Luc Classical Analysis and ODEs Representation Theory An algebraic interpretation of matrix-valued orthogonal polynomials (MVOPs) is provided. The construction is based on representations of a ($q$-deformed) Lie algebra $\mathfrak{g}$ into the algebra $\operatorname{End}_{M_n(\mathbb{C})}(M)$ of $M_n(\mathbb{C})$-linear maps over a $M_n(\mathbb{C})$-module $M$. Cases corresponding to the Lie algebras $\mathfrak{su}(2)$ and $\mathfrak{su}(1, 1)$ as well as to the $q$-deformed algebra $\mathfrak{so}_q(3)$ at $q$ a root of unity are presented; they lead to matrix analogs of the Krawtchouk, Meixner and discrete Chebyshev polynomials. |
| title | Algebraic interpretation of discrete families of matrix valued orthogonal polynomials |
| topic | Classical Analysis and ODEs Representation Theory |
| url | https://arxiv.org/abs/2510.25948 |