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The Electronic Journal of Linear AlgebraLet $\mathbb{F}$ 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 $A: V \to V$ and $A^* : V \to V$ that each act on an eigenbasis for the other in an irreducible tridiagonal fashion. Let $A,A^*$ denote a Leonard pair on
Kazumasa Nomura, Paul Terwilliger
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Dual -1 Hahn polynomials: "classical" polynomials beyond the Leonard duality [PDF]
, 2011 We introduce the -1 dual Hahn polynomials through an appropriate $q \to -1$ limit of the dual q-Hahn polynomials. These polynomials are orthogonal on a finite set of discrete points on the real axis, but in contrast to the classical orthogonal ...
Tsujimoto, Satoshi +2 more
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Forced gradings and the Humphreys-Verma conjecture
, 2012 Let $G$ be a semisimple, simply connected algebraic group defined and split over a prime field ${\mathbb F}_p$ of positive characteristic. For a positive integer $r$, let $G_r$ be the $r$th Frobenius kernel of $G$. Let $Q$ be a projective indecomposable (
Parshall, Brian, Scott, Leonard
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An integrable structure related with tridiagonal algebras
, 2004 The standard generators of tridiagonal algebras, recently introduced by Terwilliger, are shown to generate a new (in)finite family of mutually commuting operators which extends the Dolan-Grady construction.
Ahn +39 more
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Leonard pairs having LB–TD form
Linear Algebra and its Applications, 2014 Fix an algebraically closed field $\mathbb{F}$ and an integer $d \geq 3$. Let $\text{Mat}_{d+1}(\mathbb{F})$ denote the $\mathbb{F}$-algebra consisting of the $(d+1) \times (d+1)$ matrices that have all entries in $\mathbb{F}$. We consider a pair of diagonalizable matrices $A,A^*$ in $\text{Mat}_{d+1}(\mathbb{F})$, each acts in an irreducible ...
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Totally bipartite Leonard pairs and totally bipartite Leonard triples of q -Racah type
Linear Algebra and its Applications, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hou, Bo, Wang, Jing, Gao, Suogang
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Askey–Wilson relations and Leonard pairs
Discrete Mathematics, 2008 22 pages; corrected version; the example of Section 2 has the normalization consistent with the rest of the ...
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An analytical study of transport, mixing and chaos in an unsteady vortical flow [PDF]
, 1990 We examine the transport properties of a particular two-dimensional, inviscid incompressible flow using dynamical systems techniques. The velocity field is time periodic and consists of the field induced by a vortex pair plus an oscillating strainrate ...
Leonard, A., Rom-Kedar, V., Wiggins, S.
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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 ...
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The Rahman polynomials and the Lie algebra sl_3(C)
, 2010 We interpret the Rahman polynomials in terms of the Lie algebra $sl_3(C)$. Using the parameters of the polynomials we define two Cartan subalgebras for $sl_3(C)$, denoted $H$ and $\tilde{H}$.
Iliev, Plamen, Terwilliger, Paul
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