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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2011 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2011
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147385 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862619082836148224 |
|---|---|
| author | Caspers, M. |
| author_facet | Caspers, M. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T13:15:48Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147385 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T13:15:48Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Caspers, M. 2019-02-14T16:55:15Z 2019-02-14T16:55:15Z 2011 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 https://nasplib.isofts.kiev.ua/handle/123456789/147385 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. This paper is a contribution to the Special Issue “Relationship of Orthogonal Polynomials and Special Functions with Quantum Groups and Integrable Systems”. The full collection is available at http://www.emis.de/journals/SIGMA/OPSF.html.
 The author likes to thank Erik Koelink for the useful discussions and Noud Aldenhoven for
 providing Fig. 1. Also, the author benefits from a detailed referee report. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs Article published earlier |
| spellingShingle | Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs Caspers, M. |
| title | 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_short | Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs |
| title_sort | spherical fourier transforms on locally compact quantum gelfand pairs |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147385 |
| work_keys_str_mv | AT caspersm sphericalfouriertransformsonlocallycompactquantumgelfandpairs |