Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs

Symmetry, Integrability and Geometry: Methods and Applications

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

DOI  :  

来源: DOAJ

【 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