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Character Tables of Association Schemes Based on Attenuated Spaces

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Abstract

The set of subspaces of a given dimension in an attenuated space has a structure of a symmetric association scheme and this association scheme is called an association scheme based on an attenuated space. Association schemes based on attenuated spaces are generalizations of Grassmann schemes and bilinear forms schemes, and also q-analogues of nonbinary Johnson schemes. Wang, Guo, and Li computed the intersection numbers of association schemes based on attenuated spaces. The aim of this paper is to compute character tables of association schemes based on attenuated spaces using the method of Tarnanen, Aaltonen, and Goethals. Moreover, we also prove that association schemes based on attenuated spaces include as a special case the m-flat association scheme, which is defined on the set of cosets of subspaces of a constant dimension in a vector space over a finite field.

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  1. Hirotake Kurihara

    Present address: Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan

Authors and Affiliations

  1. Mathematical Institute, Tohoku University, Aramaki-Aza-Aoba 6-3, Aoba-ku, Sendai, 980-8578, Japan

    Hirotake Kurihara

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  1. Hirotake Kurihara
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Correspondence to Hirotake Kurihara.

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The author is supported by JSPS Research Fellowship.

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Kurihara, H. Character Tables of Association Schemes Based on Attenuated Spaces. Ann. Comb. 17, 525–541 (2013). https://doi.org/10.1007/s00026-013-0194-5

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  • DOI: https://doi.org/10.1007/s00026-013-0194-5

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