Almost Commutative Terwilliger Algebras of Group Association Schemes II: Primitive Idempotents

TL;DR

This paper completes the classification of primitive idempotents in almost commutative Terwilliger algebras of group association schemes by identifying the primitive idempotents for the remaining group type.

Contribution

It extends previous work by explicitly determining primitive idempotents for the last remaining group type in the classification.

Findings

Primitive idempotents identified for the fourth group type

Complete classification of primitive idempotents in almost commutative Terwilliger algebras

Enhanced understanding of algebraic structure of group association schemes

Abstract

This paper is a continuation of Almost Commutative Terwilliger Algebras of Group Association Schemes I: Classification [1]. In that paper, we found all groups G for which the Terwilliger algebra of the group association scheme, denoted T (G), is almost commutative. We also found the primitive idempotents for T (G) for three of the four types of such groups. In this paper, we determine the primitive idempotents for the fourth type.