TY - JOUR
T1 - A bilinear form relating two Leonard systems
AU - Tanaka, Hajime
PY - 2009/10/15
Y1 - 2009/10/15
N2 - 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.
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
UR - http://www.scopus.com/inward/record.url?scp=69349100071&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=69349100071&partnerID=8YFLogxK
U2 - 10.1016/j.laa.2009.06.012
DO - 10.1016/j.laa.2009.06.012
M3 - Article
AN - SCOPUS:69349100071
SN - 0024-3795
VL - 431
SP - 1726
EP - 1739
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
IS - 10
ER -