Multivariate Meixner polynomials related to holomorphic discrete series representations of SU(1,d)

Journal Article (2024)
Author(s)

Wolter Groenevelt (TU Delft - Analysis)

Joop Vermeulen (Eindhoven University of Technology)

Research Group
Analysis
DOI related publication
https://doi.org/10.1016/j.indag.2024.04.010
More Info
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Publication Year
2024
Language
English
Research Group
Analysis
Issue number
1
Volume number
36
Pages (from-to)
171-187
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Abstract

We show that Griffiths’ multivariate Meixner polynomials occur as matrix coefficients of holomorphic discrete series representations of the group 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.