Degenerate Principal Series For Symplectic And Odd-orthogonal Groups (memoirs Of The American Mathematical Society)

This memoir studies reducibility in a certain class of induced representations for $Sp_{2n}(F)$ and $SO_{2n+1}(F)$, where $F$ is $p$-adic. In particular, it is concerned with representations obtained by inducing a one-dimensional representation from a maximal parabolic subgroup (i.e., degenerate principal series representations). Using the Jacquet module techniques of Tadicacute, the reducibility points for such representations are determined. When reducible, the composition series is described, giving Langlands data and Jacquet modules for the irreducible composition factors. In this paper, we study p-adic fields, symplectic groups, orthogonal groups, and the reducibility of such representations. We determine the reducibility points, give Langlands data and Jacquet modules for each of the irreducible composition factors, and describe how they are arranged into composition series