幂等系统

摘要：

本文引入了幂等系统的概念。这个线性代数对象的动机的结构的关联方案。我们专注于一族幂等系统，据说是对称的。对称幂等系是对称结合模式的子成分代数的主模的抽象。我们详细描述了对称幂等系统。我们还考虑了一类对称幂等系统，称之为$P$ -多项式和$Q$ -多项式.在正交多项式的主题中，有一个对象称为Leonard系统。我们证明了Leonard系统本质上与对称幂等系统是一样的，对称幂等系统是$P$ -多项式和$Q$ -多项式.

英文摘要：

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 $P$-polynomial and $Q$-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 $P$-polynomial and $Q$-polynomial.

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