Representations induced from cuspidal and ladder representations of classical 𝑝-adic groups

Abstract

Let G n G_n denote either the group S p ( 2 n , F ) Sp(2n, F) or S O ( 2 n + 1 , F ) SO(2n+1, F) over a non-archimedean local field F F . We determine the composition series of representations of G n G_n induced from cuspidal and ladder representations such that the minimal exponent in the cuspidal support of the ladder representation is greater than or equal to 1 2 \frac {1}{2} .