The embeddings of the discrete series in the principal series for semisimple Lie groups of real rank one
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- by M. Welleda Baldoni Silva PDF
- 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.References
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Additional Information
- © Copyright 1980 American Mathematical Society
- 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