Matrix units associated with the split basis of a Leonard pair

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dc.creatorNomura, Kazumasa
dc.creatorTerwilliger, Paul
dc.date2006-02-19
dc.date.accessioned2026-07-07T07:03:35Z
dc.date.available2026-07-07T07:03:35Z
dc.descriptionLet $K$ denote a field, and let $V$ denote a vector space over $K$ with finite positive dimension. We consider a pair of linear transformations $A:V \to V$ and $A^*:V \to V$ that satisfy (i), (ii) below: (i) There exists a basis for $V$ with respect to which the matrix representing $A$ is irreducible tridiagonal and the matrix representing $A^*$ is diagonal. (ii) There exists a basis for $V$ with respect to which the matrix representing $A^*$ is irreducible tridiagonal and the matrix representing $A$ is diagonal. We call such a pair a {\em Leonard pair} on $V$. It is known that there exists a basis for $V$ with respect to which the matrix representing $A$ is lower bidiagonal and the matrix representing $A^*$ is upper bidiagonal. In this paper we give some formulae involving the matrix units associated with this basis.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/math/0602416
dc.identifierhttp://arxiv.org/abs/math/0602416
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/109029
dc.subjectRings and Algebras
dc.subjectQuantum Algebra
dc.subject05E35; 05E30
dc.titleMatrix units associated with the split basis of a Leonard pair
dc.typetext

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