Multivariate Meixner polynomials related to holomorphic discrete series representations of $\mathrm{SU}(1,d)$

Wolter Groenevelt; Joop Vermeulen

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arXiv · 2311.18109

Multivariate Meixner polynomials related to holomorphic discrete series representations of $\mathrm{SU}(1,d)$

Wolter Groenevelt·Joop Vermeulen

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Abstract

We show that Griffiths' multivariate Meixner polynomials occur as matrix coefficients of holomorphic discrete series representations of the group $\mathrm{SU}(1,d)$. Using this interpretation we derive several fundamental properties of the multivariate Meixner polynomials, such as orthogonality relations and difference equations. Furthermore, we also show that matrix coefficients for specific group elements lead to degenerate versions of the multivariate Meixner polynomials and their properties.

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Wolter Groenevelt, Joop Vermeulen. 2023-11-29. Multivariate Meixner polynomials related to holomorphic discrete series representations of $\mathrm{SU}(1,d)$. https://arxiv.org/abs/2311.18109

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