On the square integrability of some representatins ...



Title On the square integrability of some representatins of SU (1, 1)
Author(s) Nasser Saad
Date 1993
Abstract We survey the theory of square integrable group representations for the non-compact, semisimple lie group SU(1,1), which has three different series of representations: principal, complementary and discrete. As a result of our survey we conclude that the discrete series representations are the only ones which are square integrable in the classical sense. In addition, we study the square integrability of the principal series representation over the homogeneous spaces SU(1,1)/A and SU(1,1)/N, where A and N are closed subgroups of SU(1,1). This latter is a generalization of an earlier proposal by Perelomov.

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