## ＜学術雑誌論文＞Normalized Leonard pairs and Askey-Wilson relations

作成者 英語 Elsevier 2007-04-01 422 1 39 57 Accepted Manuscript open access (c) 2007 Elsevier B.V. MHF Preprint Series, Kyushu University ; 2005-16 Linear Algebra and its Applications || 422(1) || p39-57 http://www.math.kyushu-u.ac.jp/gakufu/ Linear Algebra and its Applications || 422(1) || p39-57 http://www.math.kyushu-u.ac.jp/gakufu/ MHF Preprint Series, Kyushu University ; 2005-16 Linear Algebra and its Applications || 422(1) || p39-57 http://www.math.kyushu-u.ac.jp/gakufu/ Let $V$ denote a vector space with finite positive dimension, and let $(A, A^*)$ denote a Leonard pair on $V$. As is known, the linear transformations $A$, $A^*$ satisfy the Askey-Wilson rel...ations $A^2A^* − \betaAA^*A + A^*A^2 − gamma(AA^* + A^*A) − sigmaA^* = gamma^*A^2 + omegaA + etaI, A^2A − \betaA^*AA^* + AA^*2 − gamma^*(A^*A + AA^*) − sigma^*A = gammaA^*2 + omegaA^* + eta^*I$, for some scalars $\beta$, $gamma$, $gamma^*$, $sigma$, $sigma^*$, $omega$, $eta$, $eta^*$. The scalar sequence is unique if the dimension of $V$ is at least 4. If $c$, $c^*$, $t$, $t^*$ are scalars and $t$, $t^*$ are not zero, then $(tA + c, t^*A^* +c^*)$ is a Leonard pair on $V$ as well. These affine transformations can be used to bring the Leonard pair or its Askey-Wilson relations into a convenient form. This paper presents convenient normalizations of Leonard pairs by the affine transformations, and exhibits explicit Askey-Wilson relations satisfied by them.続きを見る

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レコードID 3364 査読無 0024-3795 10.1016/j.laa.2005.12.033 Kyushu University 21st Century COE Program Development of Dynamic Mathematics with High Functionality 九州大学21世紀COEプログラム「機能数理学の構築と展開」 学術雑誌論文 2009.04.22 2024.01.10