Degenerate principal series and compact groups. (English) Zbl 0687.22003

Johnson, Kenneth D.

Math. Ann. 287, No. 4, 703-718 (1990).

Suppose G is one of the three groups SU(n,n), Sp(n,n) or \(Spin_ 0(n,n)\). Fix K, a maximal compact subgroup of G, and choose P to be the maximal parabolic subgroup of G such that G/P is a K-symmetric space. In this paper, we solve the problems of obtaining the complete reducibility and the unitarizability of degenerate principal series representations of G induced from representations of P that are trivial on both \(K\cap P_ 0\) and the unipotent radical of P.

Reviewer: K.D.Johnson

MSC:

22E46	Semisimple Lie groups and their representations
22C05	Compact groups

Keywords:

maximal compact subgroup; maximal parabolic subgroup; K-symmetric space; complete reducibility; unitarizability; degenerate principal series representations

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