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Hypercube and tetrahedron algebra

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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} D i=0 , 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.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050024, China

    Bo Hou & Suogang Gao

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  1. Bo Hou
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  2. Suogang Gao
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Correspondence to Bo Hou.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11471097, 11271257), the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20121303110005), the Natural Science Foundation of Hebei Province (No.A2013205021) and the Key Fund Project of Hebei Normal University (No. L2012Z01).

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Hou, B., Gao, S. Hypercube and tetrahedron algebra. Chin. Ann. Math. Ser. B 36, 293–306 (2015). https://doi.org/10.1007/s11401-015-0906-8

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  • DOI: https://doi.org/10.1007/s11401-015-0906-8

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