# Eigenspaces of symmetric graphs are not typically irreducible

## TL;DR

This paper demonstrates that for certain symmetric graphs, the eigenspaces of associated Schrödinger operators often have degeneracies exceeding what is possible under irreducible symmetry representations, challenging common assumptions.

## Contribution

The authors construct families of Schrödinger operators on symmetric graphs with eigenspaces larger than the maximal irreducible representation dimension, revealing new spectral degeneracy phenomena.

## Key findings

- Spectral degeneracies surpass irreducible representation limits
- Construction of Schrödinger operators with atypical eigenspace dimensions
- Implications for symmetry and spectral theory in graph operators

## Abstract

We construct rich families of Schr\"odinger operators on symmetric graphs, both quantum and combinatorial, whose spectral degeneracies are persistently larger than the maximal dimension of an irreducible representations of the symmetry group.