Matrix Spherical Functions for (SU( + ), S(U() × U())) : Two Specific Classes
We consider the matrix spherical function related to the compact symmetric pair (G, K) = (SU( + ), S(U()×U())). The irreducible representations (π, V) in the U() part are considered, and the induced representation Indᴳπ splits multiplicity-free. In this case, the irreducible representations in the...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2023 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2023
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211974 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Matrix Spherical Functions for (SU( + ), S(U()×U())) : Two Specific Classes. Jie Liu. SIGMA 19 (2023), 055, 33 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862628525859667968 |
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| author | Liu, Jie |
| author_facet | Liu, Jie |
| citation_txt | Matrix Spherical Functions for (SU( + ), S(U()×U())) : Two Specific Classes. Jie Liu. SIGMA 19 (2023), 055, 33 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We consider the matrix spherical function related to the compact symmetric pair (G, K) = (SU( + ), S(U()×U())). The irreducible representations (π, V) in the U() part are considered, and the induced representation Indᴳπ splits multiplicity-free. In this case, the irreducible representations in the U() part are studied. The corresponding spherical functions can be approximated in terms of the simpler matrix-valued functions. We can determine the explicit spherical functions using the action of a differential operator. We consider several cases of irreducible K representations, and the orthogonality relations are also described.
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| first_indexed | 2026-03-14T17:00:32Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211974 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T17:00:32Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Liu, Jie 2026-01-20T16:12:31Z 2023 Matrix Spherical Functions for (SU( + ), S(U()×U())) : Two Specific Classes. Jie Liu. SIGMA 19 (2023), 055, 33 pages 1815-0659 2020 Mathematics Subject Classification: 17B10; 22E46; 33C50 arXiv:2210.03041 https://nasplib.isofts.kiev.ua/handle/123456789/211974 https://doi.org/10.3842/SIGMA.2023.055 We consider the matrix spherical function related to the compact symmetric pair (G, K) = (SU( + ), S(U()×U())). The irreducible representations (π, V) in the U() part are considered, and the induced representation Indᴳπ splits multiplicity-free. In this case, the irreducible representations in the U() part are studied. The corresponding spherical functions can be approximated in terms of the simpler matrix-valued functions. We can determine the explicit spherical functions using the action of a differential operator. We consider several cases of irreducible K representations, and the orthogonality relations are also described. We thank Erik Koelink and Maarten van Pruijssen for useful discussions and feedback, and we also thank the anonymous referees for contributing to improving the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Matrix Spherical Functions for (SU( + ), S(U() × U())) : Two Specific Classes Article published earlier |
| spellingShingle | Matrix Spherical Functions for (SU( + ), S(U() × U())) : Two Specific Classes Liu, Jie |
| title | Matrix Spherical Functions for (SU( + ), S(U() × U())) : Two Specific Classes |
| title_full | Matrix Spherical Functions for (SU( + ), S(U() × U())) : Two Specific Classes |
| title_fullStr | Matrix Spherical Functions for (SU( + ), S(U() × U())) : Two Specific Classes |
| title_full_unstemmed | Matrix Spherical Functions for (SU( + ), S(U() × U())) : Two Specific Classes |
| title_short | Matrix Spherical Functions for (SU( + ), S(U() × U())) : Two Specific Classes |
| title_sort | matrix spherical functions for (su( + ), s(u() × u())) : two specific classes |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211974 |
| work_keys_str_mv | AT liujie matrixsphericalfunctionsforsusuutwospecificclasses |