Two linear transformations each tridiagonal with respect to an eigenbasis of the other; the TD–D canonical form and the LB–UB canonical form

• Published in: Journal of algebra Vol. 291; no. 1; pp. 1 - 45
• Main Author: Terwilliger, Paul
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.09.2005
• Subjects: Askey scheme; Askey–Wilson polynomials; Leonard pair; q-Racah polynomials; Tridiagonal pair; Askey scheme; q-Racah polynomials; Leonard pair; Tridiagonal pair; Askey–Wilson polynomials

Let K denote a field and let V denote a vector space over K with finite positive dimension. We consider an ordered pair of linear transformations A : V → V and B : V → V which satisfy both (i), (ii) below. (i) There exists a basis for V with respect to which the matrix representing A is irreducible...