Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs

Symmetry Integrability and Geometry-Methods and Applications

article

Martijn Caspers¹ 

[1] Radboud Universiteit Nijmegen

关键词: locally compact quantum groups;    Plancherel theorem;    Fourier transform;    spherical functions;   

DOI  :  10.3842/SIGMA.2011.087

来源: National Academy of Science of Ukraine

【 摘 要 】

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 ) together with its diagonal subgroup into a pair for which every irreducible corepresentation admits at most two vectors that are invariant with respect to the quantum subgroup. Using a Z 2 -grading, we obtain product formulae for little q -Jacobi functions.

【 授权许可】

Unknown