Irreducible representations of wedge products of table algebras and applications to association schemes

TL;DR

This paper characterizes all irreducible representations of wedge products of table algebras, provides conditions for such products, and explores applications to association schemes.

Contribution

It explicitly determines irreducible representations of wedge products and establishes criteria for their formation, advancing the understanding of algebraic structures in association schemes.

Findings

Complete classification of irreducible representations of wedge products

Necessary and sufficient conditions for a table algebra to be a wedge product

Applications to the theory of association schemes

Abstract

In this paper we first determine all irreducible representations of a wedge product of two table algebras in terms of the irreducible representations of two factors involved. Then we give some necessary and sufficient conditions for a table algebra to be a wedge product of two table algebras. Some applications to association schemes are also given.