Totally bipartite Leonard pairs and totally bipartite Leonard triples of q -Racah type
نویسندگان
چکیده
منابع مشابه
Ela Totally Bipartite/abipartite Leonard Pairs and Leonard Triples of Bannai/ito Type
This paper is about three classes of objects: Leonard pairs, Leonard triples, and the modules for a certain algebra A. Let K denote an algebraically closed field of characteristic zero. Let V denote a vector space over K with finite positive dimension. A Leonard pair on V is an ordered pair of linear transformations in End(V ) such that, for each of these transformations, there exists a basis f...
متن کامل2 00 8 Leonard pairs and the q - Racah polynomials ∗
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 → V and A : V → V that satisfy the following two conditions: (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. (ii) There exists a basis for V with respec...
متن کاملLeonard triples and hypercubes
Let V denote a vector space over C with finite positive dimension. By a Leonard triple on V we mean an ordered triple of linear operators on V such that for each of these operators there exists a basis of V with respect to which the matrix representing that operator is diagonal and the matrices representing the other two operators are irreducible tridiagonal. Let D denote a positive integer and...
متن کاملBalanced Leonard Pairs
Let K denote a field, and let V denote a vector space over K with finite positive dimension. By a Leonard pair on V we mean an ordered pair of linear transformations A : V → V and A∗ : V → V that satisfy the following two conditions: (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. (ii) There ex...
متن کامل“Leonard Pairs” in Classical Mechanics
Ġ = {G,H}. In particular, the DV F is called an integral if it has zero PB with the Hamiltonian {F,H} = 0. In this case F does not depend on t. In many problems of the classical mechanics DV form elegant algebraic structures which are closed with respect to PB. The Poisson structures with non-linear PB were discussed in [9] and [6]. Sklyanin introduced [9] the so-called quadratic Poisson algebr...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2014
ISSN: 0024-3795
DOI: 10.1016/j.laa.2014.02.002