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Degenerate principal series for symplectic and odd-orthogonal groups. (English) Zbl 0866.22016

Mem. Am. Math. Soc. 590, 100 p. (1996).
Let \(F\) be a \(p\)-adic field of characteristic \(0\). Let \(G\) be the group \(\operatorname{SO}_{2n+1}(F)\) or \(\operatorname{Sp}_{2n}(F)\). The author determines the composition series for principal series representations obtained by inducing one-dimensional representations from a maximal parabolic subgroup of \(G\). The composition factors are described in terms of their Langlands data. The author shows that the length of the composition series is \(\leq 4\). His methods are based on techniques developed before by Marko Tadić.

MSC:

22E50 Representations of Lie and linear algebraic groups over local fields
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