Noncommutative Harmonic Analysis on Quantum Hyperbolic Spaces. The Laplace-Beltrami Operator
Quantum Algebra
2017-01-02 v1 Representation Theory
Abstract
In this paper we study the Laplace-Beltrami operator on quantum complex hyperbolic spaces. We describe its action in terms of certain -difference operators of second order and prove spectral theorems for these operators. The corresponding eigenfunctions are related to Al-Salam-Chihara polynomials. The obtained Plancherel measure is related to a quantum analog for the Harish-Chandra c-function.
Keywords
Cite
@article{arxiv.1612.09412,
title = {Noncommutative Harmonic Analysis on Quantum Hyperbolic Spaces. The Laplace-Beltrami Operator},
author = {Olga Bershtein},
journal= {arXiv preprint arXiv:1612.09412},
year = {2017}
}