Abstract
compute the intertwining number of these representations, anld from these results deduce necessary and sufficient conditions for irreducibility and disjointness. For the case of representations induced from compact normlal subgroups we shall obtain certain other kinds of information. Because at one point it becomes necessary to consider projective represenitations and because the treatment of projective representations throughout offers essentially no more difficulty than that of ordinary representations, we shall in fact present these results for projective representations. We shall in general employ the terminology and definitions of [7], with two exceptions. What Mackey calls a r' representation we call a o- representation, and we shall always suppose the multipliers a are normalized, that is, we suppose a (x, x)-' 1, all x, which implies o (x, y)-1 = o(y-1, x-1), all x, y; see [5] for further
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