作成者 英語 Faculty of Mathematics, Kyushu University 九州大学大学院数理学研究院 Elsevier 2008-02-28 308 4 479 495 Author's Original open access It is known that if $(A, A^*)$ is a Leonard pair, then the linear transformations $A$, $A^*$ satisfy the Askey-Wilson relations $A^2A^* − \betaAA^*A + A^*A^2 − gamma(AA^* + A^*A) − sigmaA^* = g...amma^*A^2 + omegaA + etaI, A^*2A − \betaA^*AA^* + AA^*2 − gamma^*(A^*A + AA^*) − sigma^*A = gammaA^*2 + omegaA^* + eta^*I$, for some scalars $\beta$, $gamma$, $gamma^*$, $sigma$, $sigma^*$, $omega$, $eta$, $eta^*$. The problem of this paper is the following: given a pair of Askey-Wilson relations as above, how many Leonard pairs are there that satisfy those relations? It turns out that the answer is 5 in general. We give the generic number of Leonard pairs for each Askey-Wilson type of Askey-Wilson relations.続きを見る