Geodesic
Leonard pairs from the equitable basis of $sl_{2}$
The electronic journal of linear algebra, Tome 20 (2010), pp. 490-505.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We construct Leonard pairs from finite-dimensional irreducible sl 2 -modules, using the equitable basis for sl 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.
Classification : 17B10, 05E35, 33C45
Keywords: Lie algebra, racah polynomials, hahn polynomials, dual hahn polynomials, krawtchouk polynomials 
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     author = {Alnajjar, Hasan and Curtin, Brian},
     title = {Leonard pairs from the equitable basis of $sl_{2}$},
     journal = {The electronic journal of linear algebra},
     pages = {490--505},
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     volume = {20},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2010__20__a18/}
}
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Alnajjar, Hasan; Curtin, Brian. Leonard pairs from the equitable basis of $sl_{2}$. The electronic journal of linear algebra, Tome 20 (2010), pp. 490-505. http://geodesic.mathdoc.fr/item/ELA_2010__20__a18/