abs_vol20_pp490-505. 25KB Jun 04 2011 12:05:48 AM

ELA

LEONARD PAIRS FROM THE EQUITABLE BASIS OF

sl

₂∗

HASAN ALNAJJAR† _{AND BRIAN CURTIN}‡

Abstract. We construct Leonard pairs from finite-dimensional irreduciblesl_{2-modules, using}

the equitable basis forsl_{2. 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 (h.najjar@ju.edu.jo).}

‡_{Department of Mathematics and Statistics, University of South Florida, 4202 E. Fowler}

Ave. PHY114, Tampa, FL 33620, USA (bcurtin@math.usf.edu). Electronic Journal of Linear Algebra ISSN 1081-3810

A publication of the International Linear Algebra Society Volume 20, pp. 490-505, August 2010