Harmonic Analysis on Quantum Complex Hyperbolic Spaces

Symmetry Integrability and Geometry-Methods and Applications

article

Olga Bershtein¹  Yevgen Kolisnyk¹ 

[1] Institute for Low Temperature Physics and Engineering

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

DOI  :  10.3842/SIGMA.2011.078

来源: National Academy of Science of Ukraine

【 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.

【 授权许可】

Unknown