| Abstract: | The problem of restricting a highest weight representation of the group U(p, q) to the subgroup 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.
Partially supported by grant RFBR 98-01-00303 and the Russian program of support of leading scientific schools (grant RFBR
96-01-96249).
Moscow Institute of Electronics and Mathematics. Translated from Funktsional'nyi analiz i Ego Prilozheniya, Vol. 34, No. 3,
pp. 49–62, July–September, 2000.
Translated by Yu. A. Neretin |
