Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2011
• Main Author: Caspers, M.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2011
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147385
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs / M. Caspers // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 44 назв. — англ.

We study Gelfand pairs for locally compact quantum groups. We give an operator algebraic interpretation and show that the quantum Plancherel transformation restricts to a spherical Plancherel transformation. As an example, we turn the quantum group analogue of the normaliser of SU(1,1) in SL(2,C) to...