Degenerate Principal Series for Symplectic and Odd-Orthogonal Groups
Degenerate Principal Series for Symplectic and Odd-Orthogonal Groups By Chris Jantzen
1997 | 100 Pages | ISBN: 0821804820 | PDF | 9 MB
1997 | 100 Pages | ISBN: 0821804820 | PDF | 9 MB
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 Tadic, 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.