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Distance-regular graphs and the q-tetrahedron algebra 伊藤, 達郎 Ito, Tatsuro 58 90015909 90015909 Terwilliger, Paul 17285 Let Γ denote a distance-regular graph with classical parameters (D, b, α, β) and b ≠ 1, α = b - 1. The condition on α implies that Γ is formally self-dual. For b = q2 we use the adjacency matrix and dual adjacency matrix to obtain an action of the q-tetrahedron algebra {squared times}q on the standard module of Γ. We describe four algebra homomorphisms into {squared times}q from the quantum affine algebra Uq (over(s l, ̂)2); using these we pull back the above {squared times}q-action to obtain four actions of Uq (over(s l, ̂)2) on the standard module of Γ. © 2008 Elsevier Ltd. All rights reserved. 金沢大学理工研究域数物科学系 journal article Elsevier 2009-04-01 AM application/pdf European Journal of Combinatorics 3 30 682 697 AA00181294 0195-6698 https://kanazawa-u.repo.nii.ac.jp/record/11080/files/SC-PR-ITO-T-682.pdf https://doi.org/10.24517/00011067 http://hdl.handle.net/2297/16731 https://kanazawa-u.repo.nii.ac.jp/records/11080 eng 10.1016/j.ejc.2008.07.011 http://dx.doi.org/10.1016/j.ejc.2008.07.011 http://www.elsevier.com/locate/issn/09156698