A bilinear form relating two Leonard systems

Hajime Tanaka

doi:10.1016/j.laa.2009.06.012

A bilinear form relating two Leonard systems

Hajime Tanaka

INF - Computer and Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

Let Φ, Φ^′ be Leonard systems over a field K, and V, V^′ the vector spaces underlying Φ, Φ^′, respectively. In this paper, we introduce and discuss a balanced bilinear form on V × V^′. Such a form naturally arises in the study of Q-polynomial distance-regular graphs. We characterize a balanced bilinear form from several points of view.

Original language	English
Pages (from-to)	1726-1739
Number of pages	14
Journal	Linear Algebra and Its Applications
Volume	431
Issue number	10
DOIs	https://doi.org/10.1016/j.laa.2009.06.012
Publication status	Published - 2009 Oct 15

Keywords

Askey scheme
Distance-regular graph
Leonard system
q-Racah polynomial

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2009.06.012

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AB - Let Φ, Φ′ be Leonard systems over a field K, and V, V′ the vector spaces underlying Φ, Φ′, respectively. In this paper, we introduce and discuss a balanced bilinear form on V × V′. Such a form naturally arises in the study of Q-polynomial distance-regular graphs. We characterize a balanced bilinear form from several points of view.

KW - Askey scheme

KW - Distance-regular graph

KW - Leonard system

KW - q-Racah polynomial

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DO - 10.1016/j.laa.2009.06.012

M3 - Article

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VL - 431

SP - 1726

EP - 1739

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 10

ER -

A bilinear form relating two Leonard systems

Abstract

Keywords

ASJC Scopus subject areas

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