4 problems

The pairwise-Leonard criterion for Leonard triples
Let $V$ be a finite-dimensional vector space over $\mathbb K$ of positive dimension, and let $A,A^*,A^\varepsilon:V\to V$ be linear transformations. A Leonard pair is a pair of tra…
openFrom papersleonard-pairs orthogonal-polynomials tridiagonal-matrices
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6
The factorized $B'_2$ -Leonard pair conjecture for the quantum loop algebra construction
Let $V_{2j_1}(u)\tensor V_{2j_2}(u)$ be the tensor-product vector space, and let $(\mathcal{A}_2,\mathcal{A}_{12};\mathcal{B}_{12},\mathcal{B}_1)$ be the indicated ordered 4-tuple…
openFrom papersleonard-pairs q-racah-polynomials quantum-loop-algebras
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3
Exhaustiveness conjecture for factorized $A_2$ -Leonard pairs
A factorized $A_2$ -Leonard pair is an object defined in the paper, and Sections and give lists of examples of such pairs. Exhaustiveness conjecture. The list of factorized $A_2$ -Le…
openFrom papersleonard-pairs orthogonal-polynomials
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8
Polynomial-kind uniformity conjecture for factorized $A_2$ -Leonard pairs
A factorized $A_2$ -Leonard pair consists of compatible parameter arrays … and … where the arrays are of type II when their eigenvalues are quadratic in the index. A parameter array…
openFrom papersaskey-scheme leonard-pairs orthogonal-polynomials
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6

The pairwise-Leonard criterion for Leonard triples