Distance-Regular Graphs Related to the Quantum Enveloping Algebra of sl(2) |
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| Authors: | Brian Curtin Kazumasa Nomura |
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| Institution: | (1) Department of Mathematics, University of California, Berkeley, CA 94720, USA;(2) College of Liberal Arts and Sciences, Tokyo Medical and Dental University, Kohnodai, Ichikawa, 272, Japan |
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| Abstract: | 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  be a distance-regular graph with diameter d  3 and valency k 3, and assume is not isomorphic to the d-cube. Fix a vertex x of , and let
(x) denote the Terwilliger algebra of with respect to x. Fix any complex number q  {0, 1, –1}. Then
is generated by certain matrices satisfying the defining relations of U
q(sl(2)) if and only if is bipartite and 2-homogeneous. |
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| Keywords: | distance-regular graph Terwilliger algebra quantum group |
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