Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs
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) to...
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| Datum: | 2011 |
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| Sprache: | English |
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Інститут математики НАН України
2011
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/147385 |
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| Zitieren: | Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs / M. Caspers // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 44 назв. — англ. |
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irk-123456789-1473852019-02-15T01:24:16Z Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs Caspers, M. 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 Z₂-grading, we obtain product formulae for little q-Jacobi functions. 2011 Article Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs / M. Caspers // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 44 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 16T99; 43A90 http://dspace.nbuv.gov.ua/handle/123456789/147385 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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 Z₂-grading, we obtain product formulae for little q-Jacobi functions. |
| format |
Article |
| author |
Caspers, M. |
| spellingShingle |
Caspers, M. Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Caspers, M. |
| author_sort |
Caspers, M. |
| title |
Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs |
| title_short |
Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs |
| title_full |
Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs |
| title_fullStr |
Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs |
| title_full_unstemmed |
Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs |
| title_sort |
spherical fourier transforms on locally compact quantum gelfand pairs |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147385 |
| citation_txt |
Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs / M. Caspers // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 44 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT caspersm sphericalfouriertransformsonlocallycompactquantumgelfandpairs |
| first_indexed |
2025-07-11T01:59:48Z |
| last_indexed |
2025-07-11T01:59:48Z |
| _version_ |
1837314016142163968 |