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Knapp-Wallach Szegő integrals. II. The higher parabolic rank case


Author: B. E. Blank
Journal: Trans. Amer. Math. Soc. 300 (1987), 49-59
MSC: Primary 22E46; Secondary 22E30
MathSciNet review: 871664
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Abstract: Let $ G$ be a connected reductive linear Lie group with compact center and real rank $ l$. For each integer $ k(1 \leqslant k \leqslant l)$ and each discrete series representation $ \pi $ of $ G$, an explicit embedding of $ \pi $ into a generalized principal series representation induced from a parabolic subgroup of rank $ k$ is given. The existence of such embeddings was proved by W. Schmid. In this paper an explicit integral formula with Szegö kernel is given which provides these mappings.


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DOI: https://doi.org/10.1090/S0002-9947-1987-0871664-1
Article copyright: © Copyright 1987 American Mathematical Society