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arXiv · 2510.25948

Algebraic interpretation of discrete families of matrix valued orthogonal polynomials

Quentin Labriet·Lucia Morey·Luc Vinet
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Abstract

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.

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Quentin Labriet, Lucia Morey, Luc Vinet. 2025-10-29. Algebraic interpretation of discrete families of matrix valued orthogonal polynomials. https://arxiv.org/abs/2510.25948

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