Harmonic Analysis on Quantum Complex Hyperbolic Spaces

[摘要] In this paper we obtain some results of harmonic analysis on quantum complex hyperbolic spaces. We introduce a quantum analog for the Laplace-Beltrami operator and its radial part. The latter appear to be second order q -difference operator, whose eigenfunctions are related to the Al-Salam-Chihara polynomials. We prove a Plancherel type theorem for it.

[关键词] quantum groups;harmonic analysis on quantum symmetric spaces;q-dif ference operators;Al-Salam–Chihara polynomials;Plancherel formula