Abstract
We consider branching laws for the restriction of some irreducible unitary representations \(\varPi \) of \(G=O(p,q)\) to its subgroup \(H=O(p-1,q)\). In Kobayashi (arXiv:1907.07994, [14]), the irreducible subrepresentations of \(O(p-1,q)\) in the restriction of the unitary \(\varPi |_{O(p-1,q) }\) are determined. By considering the restriction of packets of irreducible representations we obtain another very simple branching law, which was conjectured in Ørsted–Speh (arXiv:1907.07544, [17]).
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Acknowledgments
The authors would like to acknowledge support by the MFO during research in pairs stay during which part of this work was accomplished.
The first author was partially supported by Grant-in-Aid for Scientific Research (A) (18H03669), Japan Society for the Promotion of Science.
The second author was partially supported by Simons Foundation collaboration grant, 633703.
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Kobayashi, T., Speh, B. (2020). A Hidden Symmetry of a Branching Law. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. LT 2019. Springer Proceedings in Mathematics & Statistics, vol 335. Springer, Singapore. https://doi.org/10.1007/978-981-15-7775-8_2
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DOI: https://doi.org/10.1007/978-981-15-7775-8_2
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