ELA
LEONARD PAIRS FROM THE EQUITABLE BASIS OF
sl
2∗HASAN ALNAJJAR† AND BRIAN CURTIN‡
Abstract. We construct Leonard pairs from finite-dimensional irreduciblesl2-modules, using
the equitable basis forsl2. We show that our construction yields all Leonard pairs of Racah, Hahn,
dual Hahn, and Krawtchouk type, and no other types of Leonard pairs.
Key words. Lie algebra, Racah polynomials, Hahn polynomials, Dual Hahn polynomials,
Krawtchouk polynomials.
AMS subject classifications.17B10, 05E35, 33C45.
∗Received by the editors October 5, 2009. Accepted for publication July 13, 2010. Handling
Editor: Hans Schneider.
†Department of Mathematics, University of Jordan, Amman 11942, Jordan ([email protected]).
‡Department of Mathematics and Statistics, University of South Florida, 4202 E. Fowler
Ave. PHY114, Tampa, FL 33620, USA ([email protected]). Electronic Journal of Linear Algebra ISSN 1081-3810
A publication of the International Linear Algebra Society Volume 20, pp. 490-505, August 2010
