Leonard pairs and the q-Racah polynomials
| dc.creator | Terwilliger, Paul | |
| dc.date | 2003-06-19 | |
| dc.date | 2008-07-24 | |
| dc.date.accessioned | 2026-07-07T09:52:25Z | |
| dc.date.available | 2026-07-07T09:52:25Z | |
| dc.description | 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 $A:V\to V$ and $A^*:V\to V$ that satisfy conditions (i), (ii) below. (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 respect to which the matrix representing $A$ is diagonal and the matrix representing $A^*$ is irreducible tridiagonal. We call such a pair a {\it Leonard pair} on $V$. We discuss a correspondence between Leonard pairs and a class of orthogonal polynomials consisting of the $q$-Racah polynomials and some related polynomials of the Askey scheme. For the polynomials in this class we obtain the 3-term recurrence, difference equation, Askey-Wilson duality, and orthogonality in a uniform manner using the corresponding Leonard pair. | |
| dc.description | 44 pages. Revised version with organization adjusted | |
| dc.identifier | https://arxiv.org/abs/math/0306301 | |
| dc.identifier | http://arxiv.org/abs/math/0306301 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165590 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Mathematical Physics | |
| dc.subject | Combinatorics | |
| dc.subject | 05E35; 05E30, 33C45,33D45 | |
| dc.title | Leonard pairs and the q-Racah polynomials | |
| dc.type | text |