Leonard pairs and the q-Racah polynomials
Terwilliger, Paul
arXiv, 0306301 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2003-06-19
Classification:  Mathematics - Quantum Algebra,  Mathematical Physics,  Mathematics - Combinatorics,  05E35,  05E30, 33C45,33D45 
@article{0306301,
     author = {Terwilliger, Paul},
     title = {Leonard pairs and the q-Racah polynomials},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0306301}
}

Terwilliger, Paul. Leonard pairs and the q-Racah polynomials. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0306301/