Introduction to Leonard pairs

By Paul M. Terwilliger. 2003

111 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/73bc362c29ae807c0a0638995703e3569896c1ef

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In Computational Theory and Mathematics

In Discrete Mathematics and Combinatorics

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Citations in the corpus

LEONARD PAIRS AND THE ASKEY-WILSON RELATIONS (2003, background): “Leonard pairs occur in combinatorics [3, 4, 16, 26, 33], representation theory [6, 7, 8, 19, 20, 21, 22, 23, 25, 33], and the theory of orthogonal polynomials [2, 24, 33, 36, 37].”
Tridiagonal pairs of q-Racah type (2008, background): “As research progressed, connections were found to representation theory [1,4,16,20,23,25,27,28,31–33,47,49,50,54,59], partially ordered sets [55], the bispectral problem [17–19, 61], statistical mechanical models [4–10, 13–15, 48], and classical mechanics [62].”
TWO NON-NILPOTENT LINEAR TRANSFORMATIONS THAT SATISFY THE CUBIC q-SERRE RELATIONS (2005, unknown): “A recent topic of research concerns the Leonard pairs [23], [37], [39], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [53], [54] and the closely related tridiagonal pairs [1], [2], [24], [25], [26], [34], [35], [36].”
Two linear transformations each tridiagonal with respect to an eigenbasis of the other: comments on the split decomposition (2003, unknown): “We begin by recalling the notion of a Leonard pair [6], [12], [13], [14], [15], [16], [17], [18].”
Finite-Dimensional Irreducible Modules for the Three-Point 𝔰𝔩2 Loop Algebra (2007, background): “ξ).viσ ξ∈ ⊠, u,v∈ V. We remark on our motivation to investigate ⊠. This has to do with the tridiagonal pairs [19], [20], [21], [22] and the closely related Leonard pairs [27], [28], [29], [35], [36], [37], [39], [40]. A Leonard pair is a pair of semisimple linear transformations on a ﬁnite-dimension”
The shape of a tridiagonal pair (2003, unknown): “See [11], [13], [14], [15], [16], [17], [18], [19], [20] for more information about Leonard pairs.”
Tridiagonal pairs and the quantum affine algebra Uq(sl2) (代数的組合せ論) (2005, unknown): “See [8], [12], [13], [14], [15], [16], [17], [19], [20] for more information about Leonard pairs.”
Two linear transformations each tridiagonal with respect to an eigenbasis of the other; the TD- D canonical form and the LB- UB canonical form (2003, unknown): “We begin by recalling the notion of a Leonard pair [16], [27], [28], [29], [35], [36].”
An Algebraic Approach to the Askey Scheme of Orthogonal Polynomials (2006, unknown): “These notes are based on the papers [45], [46], [47], [79], [80], [81], [82], [ 83 ], [84], [85], [86], [87], [88].”
Linear transformations that are tridiagonal with respect to both eigenbases of a Leonard pair (2006, background): “ In a Leonard pair (A,A∗) the linear transformations A and A∗ are arbitrary subject to (i) and (ii) above. We refer the reader to [3], [9], [12], [13], [14], [15], [16], [17], [18], [19], [21], [22], [23], [24], [25], [26], [27], [28], [30], [31] for background on Leonard pairs. We especially recomm”
Two linear transformations each tridiagonal with respect to an eigenbasis of the other: An Algebraic approach to the Askey scheme of orthogonal polynomials (2004, unknown): “ch . . . . . . . . . . . . . . . . 63 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 1 Leonard pairs These notes are based on the papers [46], [47], [48], [91], [92], [93], [94], [95], [96], [97], [98], [99], [100]. We begin by recalling the notion of a Leonard pair. We will use”