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

Blank, B. E.

doi:10.1090/S0002-9947-1987-0871664-1

Knapp-Wallach Szegő integrals. II. The higher parabolic rank case
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by B. E. Blank PDF

Trans. Amer. Math. Soc. 300 (1987), 49-59 Request permission

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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