Jacquet modules of principal series generated by the trivial \(K\)-type
Let \(G\) be a real semisimple Lie group and \(X\) be an irreducible admissible representation of \(G\). In 1980, \textit{W. Casselman} [Proc. int. Congr. Math., Helsinki 1978, Vol.~2, 557--563 (1980; Zbl 0425.22019)] introduced the Jacquet module \(J(X)\) of \(X\). The structure of the Jacquet module \(J(X)\) turns out to be quite complicated and can only be determined in very special cases. If \(G\) has real rank 1, then the structure of \(J(X)\) is known in detail [see \textit{D. H. Collingwood}, Representations of rank one Lie groups. Research Notes in Mathematics, 137. Boston - London - Melbourne (1985; Zbl 0647.22007)]. In the paper under review the author determines generators of the Jacquet module of a principal series representation by the trivial \(K\)-type.
scientific article; zbMATH DE number 5543226
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