caa a22 4500 463178149 CHVBK 20180406164831.0 cr unu---uuuuu 170326e20070601xx s 000 0 eng 10.1007/s11139-006-0255-z doi (NATIONALLICENCE)springer-10.1007/s11139-006-0255-z Curtin Brian Department of Mathematics, University of South Florida, 4202 E. Fowler Ave., PHY114, 33620, Tampa, Florida aut Spin Leonard pairs [Elektronische Daten] [Brian Curtin] Let $${\mathbb K}$$ denote a field, and let V denote a vector space over $${\mathbb K}$$ of finite positive dimension. A pair A, A* of linear operators on V is said to be a Leonard pair on V whenever for each B∈{A, A*}, there exists a basis of V with respect to which the matrix representing B is diagonal and the matrix representing the other member of the pair is irreducible tridiagonal. A Leonard pair A, A* on V is said to be a spin Leonard pair whenever there exist invertible linear operators U, U* on V such that UA = A U, U*A* = A*U*, and UA* U −1 = U*−1 AU*. In this case, we refer to U, U* as a Boltzmann pair for A, A*. We characterize the spin Leonard pairs. This characterization involves explicit formulas for the entries of the matrices that represent A and A* with respect to a particular basis. The formulas are expressed in terms of four algebraically independent parameters. We describe all Boltzmann pairs for a spin Leonard pair in terms of these parameters. We then describe all spin Leonard pairs associated with a given Boltzmann pair. We also describe the relationship between spin Leonard pairs and modular Leonard triples. We note a modular group action on each isomorphism class of spin Leonard pairs. Springer Science + Business Media, LLC, 2006 Modular Leonard triple nationallicence Orthogonal polynomial nationallicence Modular group nationallicence The Ramanujan Journal Kluwer Academic Publishers 13/1-3(2007-06-01), 319-332 1382-4090 13:1-3<319 2007 13 11139 https://doi.org/10.1007/s11139-006-0255-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11139-006-0255-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Curtin Brian Department of Mathematics, University of South Florida, 4202 E. Fowler Ave., PHY114, 33620, Tampa, Florida aut NATIONALLICENCE 773 0- The Ramanujan Journal Kluwer Academic Publishers 13/1-3(2007-06-01), 319-332 1382-4090 13:1-3<319 2007 13 11139 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer