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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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

Author: M. Welleda Baldoni Silva
Journal: Trans. Amer. Math. Soc. 261 (1980), 303-368
MSC: Primary 22E46; Secondary 22E30
MathSciNet review: 580893
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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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Keywords: Representations of semisimple Lie groups, real rank, branching theorems, minimal <I>K</I>-types, irreducible component
Article copyright: © Copyright 1980 American Mathematical Society