Association schemes all of whose symmetric fusion schemes are integral

TL;DR

This paper characterizes association schemes where all symmetric fusion schemes have integral eigenvalues and classifies those derived from regular group actions.

Contribution

It provides a characterization and classification of association schemes with integral eigenvalues in all symmetric fusion schemes, especially those from regular group actions.

Findings

Identifies conditions for association schemes with integral eigenvalues

Classifies schemes from regular group actions based on these properties

Advances understanding of the structure of such association schemes

Abstract

In this paper we aim to characterize association schemes all of whose symmetric fusion schemes have only integral eigenvalues, and classify those obtained from a regular action of a finite group by taking its orbitals.