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arXiv · 1104.2459

Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs

Martijn Caspers
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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.

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Martijn Caspers. 2011-04-13. Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs. https://doi.org/10.3842/sigma.2011.087

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