# Degenerate principal series in the general case

## TL;DR

This paper classifies all composition factors of degenerate principal series representations for certain classical groups over non-archimedean fields, expanding understanding of their structure using advanced involution techniques.

## Contribution

It provides a complete determination of composition factors for degenerate principal series in the general case, employing the Aubert involution and existing irreducibility results.

## Key findings

- All composition factors of degenerate principal series are identified.
- Methods combine Aubert involution with known irreducibility results.
- Results apply to groups SO(2n+1, F), Sp(2n, F), and GSpin(2n+1, F).

## Abstract

Let $G_n$ denote either the group $SO(2n+1, F)$, $Sp(2n, F)$, or $GSpin(2n+1, F)$ over a non-archimedean local field of characteristic different than two. We determine all composition factors of degenerate principal series of $G_n$, using methods based on the Aubert involution and known results on irreducible subquotiens of the generalized principal series of particular type.