The embeddings of the discrete series in the principal series for semisimple Lie groups of real rank one

Baldoni Silva, M. Welleda

doi:10.1090/S0002-9947-1980-0580893-X

The embeddings of the discrete series in the principal series for semisimple Lie groups of real rank one
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Trans. Amer. Math. Soc. 261 (1980), 303-368 Request permission

Abstract:

We consider the problem of finding all the “embeddings” of a discrete series representation in the principal series in the case of a simple real Lie group G of real rank one. More precisely, we solve the problem when G is $\operatorname {Spin} (2n, 1),{\text {SU}}(n, 1), {\text {SP}}(n, 1) {\text {or}} {F_4} (n \geqslant 2)$. The problem is reduced to considering only discrete series representations with trivial infinitesimal character, by means of tensoring with finite dimensional representations. Various other techniques are employed.

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