Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs

Details Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs

2011-04-13

arxiv.org/abs/1104.2459v2

SIGMA 7 (2011), 087, 39 pages

Mathematics

Operator Algebras

Scientific paper

10.3842/SIGMA.2011.087

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.

Affiliated with

Also associated with

No associations

Rating

Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-218634