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| Summary: | 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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| ISSN: | 1815-0659 |