Three Mutually Adjacent Leonard Pairs

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dc.creatorHartwig, Brian
dc.date2005-08-22
dc.date.accessioned2026-07-07T05:22:35Z
dc.date.available2026-07-07T05:22:35Z
dc.descriptionLet (A,B) and (C,D) denote Leonard pairs on V. We say these pairs are adjacent whenever each basis for V which is standard for (A,B) (resp. (C,D)) is split for (C,D) (resp. (A,B)). Our main results are as follows: Theorem 1. There exists at most 3 mutually adjacent Leonard pairs on V provided the dimension of V is at least 2. Theorem 2. Let (A,B), (C,D), and (E,F) denote three mutually adjacent Leonard pairs on V. There for each of these pairs, the eigenvalue sequence and dual eigenvalue sequence are in arithmetic progression. Theorem 3. Let (A,B) denote a Leonard pair on V whose eigenvalue sequence and dual eigenvalue sequence are in arithmetic progression. Then there exist Leonard pairs (C,D) and (E,F) on V such that (A,B), (C,D), and (E,F) are mutually adjacent.
dc.description19 pages. To be published in Linear Algebra and it Applications
dc.identifierhttps://arxiv.org/abs/math/0508415
dc.identifierhttp://arxiv.org/abs/math/0508415
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76116
dc.subjectCommutative Algebra
dc.subjectCombinatorics
dc.subjectRepresentation Theory
dc.titleThree Mutually Adjacent Leonard Pairs
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