Group-case commutative association schemes and their character tables

TL;DR

This paper surveys progress in classifying primitive commutative association schemes, focusing on identifying sources, collecting known group-case schemes, and computing their character tables to aid systematic understanding.

Contribution

It summarizes recent advances in constructing character tables for group-case primitive commutative association schemes and highlights open problems in the field.

Findings

Progress in classifying primitive commutative association schemes

Compilation of known group-case schemes and their character tables

Identification of open problems for future research

Abstract

Leading towards the classification of primitive commutative association schemes as the ultimate goal, Bannai and some of his school have been trying to * identify the major sources of (primitive) commutative association schemes, * collect known group-case primitive commutative association schemes, and * compute their character tables over the last twenty years. The construction of their character tables are important first step for a systematic study of such association schemes and towards the classification of those schemes. In this talk, we briefly survey the progress made in this direction of research, and list some open problems.