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Leonard Pairs from 24 Points of View

Rocky Mountain Journal of Mathematics, 2002
Let $K$ 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 both conditions below: (i) There exists a basis for $V$ with respect to which the matrix representing $A$ is diagonal and the matrix representing $A^*$ is irreducible ...
Paul Terwilliger
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Factorized $$A_2$$-Leonard pair

Ramanujan Journal
33 ...
Meri Zaimi, Nicolas Crampe
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The end-parameters of a Leonard pair

Linear Algebra and Its Applications, 2014
Fix an algebraically closed field $\F$ and an integer $d \geq 3$. Let $V$ be a vector space over $\F$ with dimension $d+1$. A Leonard pair on $V$ is a pair of diagonalizable linear transformations $A: V \to V$ and $A^* : V \to V$, each acting in an irreducible tridiagonal fashion on an eigenbasis for the other one.
Kazumasa Nomura
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Leonard pairs, spin models, and distance-regular graphs [PDF]

Journal of Combinatorial Theory - Series A, 2021
A Leonard pair is an ordered pair of diagonalizable linear maps on a finite-dimensional vector space, that each act on an eigenbasis for the other one in an irreducible tridiagonal fashion. In the present paper we consider a type of Leonard pair, said to have spin. The notion of a spin model was introduced by V.F.R.
Paul Terwilliger, Kazumasa Nomura
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Three mutually adjacent Leonard pairs

Linear Algebra and Its Applications, 2005
Let (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)
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Spin Leonard pairs

The Ramanujan Journal, 2007
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Leonard triples extended from a given totally almost bipartite Leonard pair of Bannai/Ito type

Linear Algebra and Its Applications, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Suogang Gao
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ON THE WITT INDEX OF THE BILINEAR FORM DETERMINED BY A LEONARD PAIR

Journal of Algebra and Its Applications, 2008
Let a,b,d be nonnegative integers such that a + b = d + 1. Let ℝ be the field of real numbers. We prove that there is always a Leonard pair A, A⋆ of d + 1 by d + 1 matrices over ℝ such that the associated bilinear form of P. Terwilliger on ℝd + 1 has the Witt index a - b.
Tang, G., Tan, Y. J.
openaire   +1 more source

A rank two Leonard pair in Terwilliger algebras of Doob graphs

Journal of Combinatorial Theory - Series A
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John Vincent Morales
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