Representations of the alternating group which are irreducible over subgroups. II

TL;DR

This paper proves that non-trivial representations of the alternating group become reducible when restricted to certain primitive subgroups isomorphic to smaller alternating groups.

Contribution

It establishes a new reducibility criterion for alternating group representations over primitive subgroups isomorphic to smaller alternating groups.

Findings

Non-trivial representations of A_n are reducible over primitive A_m subgroups.

The result applies to all non-trivial representations of the alternating group.

Provides insight into the structure of representations when restricted to specific subgroups.

Abstract

We prove that non-trivial representations of the alternating group $A_n$ are reducible over a primitive proper subgroup which is isomorphic to some alternating group $A_m$.