Geodesic
Distance-regular graphs related to the quantum enveloping algebra of $sl(2)$
Journal of Algebraic Combinatorics, Tome 12 (2000) no. 1, pp. 25-36.

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

Summary: We investigate a connection between distance-regular graphs and $U _{q}( sl(2))$, the quantum universal enveloping algebra of the Lie algebra $sl(2)$. Let $T = T( x)$ mathcalT = mathcalT$(x) ( x)$ denote the Terwilliger algebra of $T$ mathcalT is generated by certain matrices satisfying the defining relations of $U _{q}( sl(2))$ if and only if $Gamma$ is bipartite and 2-homogeneous.
Keywords: distance-regular graph, Terwilliger algebra, quantum group 
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     title = {Distance-regular graphs related to the quantum enveloping algebra of $sl(2)$},
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Curtin, Brian; Nomura, Kazumasa. Distance-regular graphs related to the quantum enveloping algebra of $sl(2)$. Journal of Algebraic Combinatorics, Tome 12 (2000) no. 1, pp. 25-36. http://geodesic.mathdoc.fr/item/JAC_2000__12_1_a5/