The Degenerate Principal Series Representations of Exceptional Groups of Type $E_7$ over $p$-adic Fields

TL;DR

This paper investigates the structure of degenerate principal series representations of split, simply-connected exceptional groups of type E7 over p-adic fields, focusing on reducibility points and subrepresentations.

Contribution

It provides a detailed analysis of reducibility and subrepresentation structure for E7 p-adic groups, a topic not extensively explored before.

Findings

Identified reducibility points of the representations.

Described the maximal semi-simple subrepresentations.

Enhanced understanding of E7 representation theory over p-adic fields.

Abstract

In this paper, we study the degenerate principal series of a split, simply-connected, simple p-adic group of type $E_7$. We determine the points of reducibility and the maximal semi-simple subrepresentation at each point.