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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
DOI: https://doi.org/10.1090/S0002-9947-1980-0580893-X
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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1980-0580893-X
Keywords: Representations of semisimple Lie groups, real rank, branching theorems, minimal K-types, irreducible component
Article copyright: © Copyright 1980 American Mathematical Society