Geodesic
Idempotent systems
Nomura, Kazumasa1 ; Terwilliger, Paul2
1 Tokyo Medical and Dental University Kohnodai, Ichikawa 272-0827, Japan
2 University of Wisconsin Dept. of mathematics 480 Lincoln Drive Madison, WI 53706 USA
Algebraic Combinatorics, Tome 4 (2021) no. 2, pp. 329-357 Cet article a éte moissonné depuis la source Numdam

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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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DOI : 10.5802/alco.159
Classification : 17B37, 15A21
Keywords: idempotent system, association scheme, Leonard pair

Nomura, Kazumasa 1 ; Terwilliger, Paul 2

1 Tokyo Medical and Dental University Kohnodai, Ichikawa 272-0827, Japan
2 University of Wisconsin Dept. of mathematics 480 Lincoln Drive Madison, WI 53706 USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Nomura, Kazumasa; Terwilliger, Paul. Idempotent systems. Algebraic Combinatorics, Tome 4 (2021) no. 2, pp. 329-357. doi: 10.5802/alco.159

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