The classification of Leonard triples of QRacah type

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Let K denote an algebraically closed field. Let V denote a vector space over K with finite positive dimension. By a Leonard triple on V we mean an ordered triple of linear transformations in End(V) such that for each of these transformations there exists a basis of V with respect to which the matrix representing that transformation is diagonal and the matrices representing the other two transformations are irreducible tridiagonal. There is a family of Leonard triples said to have QRacah type. This is the most general type of Leonard triple. We classify the Leonard triples of QRacah type up to isomorphism. We show that any Leonard triple of QRacah type satisfies the Z3-symmetric Askey-Wilson relations.

Original languageEnglish
Pages (from-to)1442-1472
Number of pages31
JournalLinear Algebra and Its Applications
Issue number5
StatePublished - 1 Mar 2012


  • Askey-Wilson relations
  • Leonard triples


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