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Representations of \(p\)-adic symplectic groups. (English) Zbl 0797.22008
For a nonarchimedean local field of characteristic \(\neq 2\) there are given criteria for the reducibility of principal series representations of the groups \(\text{Sp}(n,F)\) and \(\text{GSp}(n,F)\). Further all square integrable representations of \(\text{GSp}(n,F)\) which may be obtained as subquotients of principal series representations induced by regular characters are described explicitly. At last the restriction from \(\text{GSp}(n,F)\) to \(\text{Sp}(n,F)\) is investigated for square integrable representations. The restricted representation splits without multiplicities and a parametrization of the irreducible pieces is given.

MSC:
22E50 Representations of Lie and linear algebraic groups over local fields
22E35 Analysis on \(p\)-adic Lie groups
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