Results 1 to 10 of about 206,636 (137)
Special Matrices, 2019 Let F denote a field and let V denote a vector space over F with finite positive dimension. Consider a pair A, A* of diagonalizable F-linear maps on V, each of which acts on an eigenbasis for the other one in an irreducible tridiagonal fashion.
Nomura Kazumasa, Terwilliger Paul
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Affine transformations of a Leonard pair [PDF]
The Electronic Journal of Linear Algebra, 2006 Let $K$ denote a field and let $V$ denote a vector space over $K$ with finite positive dimension. We consider an ordered pair of linear transformations $A : V \to V$ and $A^* : V \to V$ that satisfy (i) and (ii) below: (i) There exists a basis for $V ...
Nomura, Kazumasa, Terwilliger, Paul
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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.
Nomura, Kazumasa, Terwilliger, Paul
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Frontiers in Research Metrics and Analytics, 2023 In this chapter, I use methods drawn from literary analysis to bear on artificial scarcity and explore how literary and legal storytelling engages in scarcity mongering.
Zahr K. Said
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LEONARD PAIRS AND THE ASKEY–WILSON RELATIONS [PDF]
Journal of Algebra and Its Applications, 2004 Let K denote a field and let V denote a vector space over K with finite positive dimension. We consider an ordered pair of linear transformations A:V→V and A*:V→V which satisfy the following two properties:(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.
Terwilliger, Paul, Vidunas, Raimundas
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Compatibility and companions for Leonard pairs
The Electronic Journal of Linear Algebra, 2022 In this paper, we introduce the concepts of compatibility and companion for Leonard pairs. These concepts are roughly described as follows. Let $\mathbb{F}$ denote a field, and let $V$ denote a vector space over $\mathbb{F}$ with finite positive dimension.A Leonard pair on $V$ is an ordered pair of diagonalizable $\mathbb{F}$-linear maps $A : V \to V ...
Kazumasa Nomura, Paul Terwilliger
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A Linear Map Acts as a Leonard Pair with Each of the Generators of Usl2
International Journal of Mathematics and Mathematical Sciences, 2020 Let ℱ denote an algebraically closed field with a characteristic not two. Fix an integer d≥3; let x, y, and z be the equitable basis of sl2 over ℱ. Let V denote an irreducible sl2-module with dimension d+1; let A∈EndV. In this paper, we show that if each
Hasan Alnajjar
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Linear Algebra and its Applications, 2007 20 ...
Nomura, Kazumasa, Terwilliger, Paul
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Cyclic tridiagonal pairs, higher order Onsager algebras and orthogonal polynomials [PDF]
, 2016 The concept of cyclic tridiagonal pairs is introduced, and explicit examples are given. For a fairly general class of cyclic tridiagonal pairs with cyclicity N, we associate a pair of `divided polynomials'. The properties of this pair generalize the ones
Baseilhac, P. +2 more
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Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz
Nuclear Physics B, 2019 An operator of Heun-Askey-Wilson type is diagonalized within the framework of the algebraic Bethe ansatz using the theory of Leonard pairs. For different specializations and the generic case, the corresponding eigenstates are constructed in the form of ...
Pascal Baseilhac, Rodrigo A. Pimenta
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