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Abstract
Let D be an integer at least 3 and let H(D, 2) denote the hypercube. It is known that H(D, 2) is a Q-polynomial distance-regular graph with diameter D, and its eigenvalue sequence and its dual eigenvalue sequence are all {D − 2i} i=0 D, Suppose that ⊠ denotes the tetrahedron algebra. In this paper, the authors display an action of ⊠ on the standard module V of H(D, 2). To describe this action, the authors define six matrices in Mat X(ℂ), called $A,A^* ,B,B^* ,K,K^* .$ Moreover, for each matrix above, the authors compute the transpose and then compute the transpose of each generator of ⊠ on V.
Keywords
Tetrahedron algebra
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Hypercube
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Distance-regular graph
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Onsager algebra
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Bo Hou, Suogang Gao.
Hypercube and tetrahedron algebra.
Chinese Annals of Mathematics, Series B, 2015, 36(2): 293-306 DOI:10.1007/s11401-015-0906-8
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