Geodesic
On the Separation of Spectra in the Analysis of Berezin Kernels
Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 3, pp. 49-62

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The problem of restricting a highest weight representation of the group $\operatorname{U}(p,q)$ to the subgroup $\operatorname{O}(p,q)$ is considered. This restriction has an intricate spectrum that contains representations of different types. We construct a decomposition of this representation into reducible representations each of which has a single-type spectrum. Some integrals over classical groups are also calculated; these integrals generalize those of Hua. 
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     author = {Yu. A. Neretin},
     title = {On the {Separation} of {Spectra} in the {Analysis} of {Berezin} {Kernels}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     number = {3},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2000_34_3_a4/}
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Yu. A. Neretin. On the Separation of Spectra in the Analysis of Berezin Kernels. Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 3, pp. 49-62. http://geodesic.mathdoc.fr/item/FAA_2000_34_3_a4/