Results 51 to 60 of about 206,636 (137)

Transition maps between the 24 bases for a Leonard pair

Linear Algebra and its Applications, 2009
28 ...
Nomura, Kazumasa, Terwilliger, Paul
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Matrix units associated with the split basis of a Leonard pair

Linear Algebra and its Applications, 2006
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 (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 ...
Nomura, Kazumasa, Terwilliger, Paul
openaire   +3 more sources

Leonard pairs having zero-diagonal TD-TD form

Linear Algebra and its Applications, 2015
Fix an algebraically closed field $\mathbb{F}$ and an integer $n \geq 1$. Let $\text{Mat}_n(\mathbb{F})$ denote the $\mathbb{F}$-algebra consisting of the $n \times n$ matrices that have all entries in $\mathbb{F}$. We consider a pair of diagonalizable matrices in $\text{Mat}_{n}(\mathbb{F})$, each acting in an irreducible tridiagonal fashion on an ...
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Krawtchouk polynomials, the Lie algebra $\mathfrak{sl}_2$, and Leonard pairs

, 2012
A Leonard pair is a pair of diagonalizable linear transformations of a finite-dimensional vector space, each of which acts in an irreducible tridiagonal fashion on an eigenbasis for the other one. In the present paper we give an elementary but comprehensive account of how the following are related: (i) Krawtchouk polynomials; (ii) finite-dimensional ...
Nomura, Kazumasa, Terwilliger, Paul
openaire   +3 more sources

A characterization of Leonard pairs using the parameters $\{a_i\}_{i=0}^{d}$

Linear Algebra and its Applications, 2012
21 pages.
openaire   +2 more sources

Spin Leonard pairs and the zero diagonal space

We consider a Leonard pair $A, A^*$ of linear maps on a vector space $V$ that has finite positive dimension. This Leonard pair $A,A^*$ is said to have spin whenever there exist invertible linear maps $W : V \to V$ and $W^* : V \to V$ such that $W A = A W$ and $W^* A^* = A^* W^*$ and $W A^* W^{-1} = (W^*)^{-1} A W^*$.
Nomura, Kazumasa, Terwilliger, Paul
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A characterization of Leonard pairs using the notion of a tail

Linear Algebra and its Applications, 2011
Let $V$ denote a vector space 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 $V$ with respect to which the matrix representing $A$ is irreducible tridiagonal and the matrix representing $A^*$ is diagonal.
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Leonard triples from Leonard pairs constructed from the standard basis of the Lie algebra sl2

Linear Algebra and its Applications
AbstractLet K denote an algebraically closed field of characteristic zero and d⩾3 denote an integer. An ordered pair of matrices A,A∗ is a Leonard pair on the vector space Kd+1 if we can find invertible matrices S1 and S2∈Md+1(K) such that (i) S1-1AS1 is diagonal and S1-1A∗S1 is irreducible tridiagonal, and (ii) S2-1A∗S2 is diagonal and S2-1AS2 is ...
Balmaceda, Jose Maria P., Maralit, Jryl P.   +1 more
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Krawtchouk polynomials, the Lie algebra sl2, and Leonard pairs

Linear Algebra and its Applications
AbstractA Leonard pair is a pair of diagonalizable linear transformations of a finite-dimensional vector space, each of which acts in an irreducible tridiagonal fashion on an eigenbasis for the other one. In the present paper we give an elementary but comprehensive account of how the following are related: (i) Krawtchouk polynomials; (ii) finite ...
Nomura, Kazumasa, Terwilliger, Paul
openaire   +1 more source

A characterization of bipartite Leonard pairs using the notion of a tail

Linear Algebra and its Applications, 2014
21 pages.
openaire   +2 more sources