Idempotent systems
Rings and Algebras
2020-05-01 v1
Abstract
In this paper we introduce the notion of an idempotent system. This linear algebraic object is motivated by the structure of an association scheme. We focus on a family of idempotent systems, said to be symmetric. A symmetric idempotent system is an abstraction of the primary module for the subconstituent algebra of a symmetric association scheme. We describe the symmetric idempotent systems in detail. We also consider a class of symmetric idempotent systems, said to be -polynomial and -polynomial. In the topic of orthogonal polynomials there is an object called a Leonard system. We show that a Leonard system is essentially the same thing as a symmetric idempotent system that is -polynomial and -polynomial.
Cite
@article{arxiv.2004.14997,
title = {Idempotent systems},
author = {Kazumasa Nomura and Paul Terwilliger},
journal= {arXiv preprint arXiv:2004.14997},
year = {2020}
}