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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:
 2.2e+51 Representations of Lie and linear algebraic groups over local fields 2.2e+36 Analysis on $$p$$-adic Lie groups
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