|
This article is cited in 3 scientific papers (total in 3 papers)
Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs
Martijn Caspers Radboud Universiteit Nijmegen, IMAPP, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
Abstract:
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 $SL(2,\mathbb C$) 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 $\mathbb Z_2$-grading, we obtain product formulae for little $q$-Jacobi functions.
Keywords:
locally compact quantum groups; Plancherel theorem; Fourier transform; spherical functions.
Received: April 14, 2011; in final form August 30, 2011; Published online September 6, 2011
Citation:
Martijn Caspers, “Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs”, SIGMA, 7 (2011), 087, 39 pp.
Linking options:
https://www.mathnet.ru/eng/sigma645 https://www.mathnet.ru/eng/sigma/v7/p87
|
Statistics & downloads: |
Abstract page: | 194 | Full-text PDF : | 59 | References: | 21 |
|