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

TL;DR

This paper analyzes the structure of induced representations of classical p-adic groups, specifically Sp and SO groups, from cuspidal and ladder representations with certain support conditions.

Contribution

It determines the composition series of these induced representations, providing new insights into their structure based on the minimal exponent in the cuspidal support.

Findings

Explicit composition series for certain induced representations

Conditions on the minimal exponent in cuspidal support

Enhanced understanding of representation structure in classical p-adic groups

Abstract

Let $G_n$ denote either the group $Sp(2n, F)$ or $SO(2n+1, F)$ over a non-archimedean local field $F$. We determine the composition series of representations of $G_n$ 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 $\frac{1}{2}$.