The Norton algebra of a $Q$-polynomial distance-regular graph

TL;DR

This paper explores the Norton algebra linked to a specific idempotent in a distance-regular graph, providing a new formula for its algebraic product that enhances understanding of its structure.

Contribution

It introduces an explicit and elegant formula for the Norton algebra product associated with a $Q$-polynomial primitive idempotent in distance-regular graphs.

Findings

Derived a formula for the Norton algebra product

Enhanced understanding of algebraic structure in distance-regular graphs

Potential applications in algebraic combinatorics

Abstract

We consider the Norton algebra associated with a $Q$-polynomial primitive idempotent of the adjacency matrix for a distance-regular graph. We obtain a formula for the Norton algebra product that we find attractive.