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Zbl 0694.22012
Li, Jian-Shu
On the classification of irreducible low rank unitary representations of classical groups. (English)
[J] Compos. Math. 71, No.1, 29-48 (1989). ISSN 0010-437X; ISSN 1570-5846/e

The notion of low rank representation was introduced in the case of the symplectic group over a local field by {\it R. Howe} [Harmonic Analysis, Cortona 1984; Symp. Math. 29, 197-204 (1987; Zbl 0648.22008)]. In the present paper the author extends this theory to all type I classical groups. As a main result, he shows that for such a group, the unitary, low rank representations constructed in a previous paper [Invent. Math. 97, 237-255 (1989; see the preceding review Zbl 0694.22011)] do exhaust all the irreducible, low rank representations of G. He also introduces the notion of distinguished representation and gives a characterization of them in certain cases. These representations have applications to the theory of automorphic forms [see {\it R. Howe}, {\it I. Piatetski- Shapiro}, Proc. Symp. Pure Math. 33, 315-322 (1979; Zbl 0423.22018)].
[R.Miatello]

MSC 2000:: *22E50 Repres. of Lie and linear algebraic groups over local fields

Keywords: symplectic group; local field; type I classical groups; low rank representations

Citations: Zbl 0648.22008; Zbl 0694.22011; Zbl 0423.22018

Cited in: Zbl 1187.22013 Zbl 0694.22011

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