Abstract
By using the character tables of known commutative association schemes, we can, in many instances, construct some new commutative association schemes as their subschemes. In particular, we obtain many new non-group-case association schemes from the group association schemes of finite simple groups. Although examples worked out in this paper are limited to some special cases, it might be possible that this phenomenon occurs universally for all the group association schemes of finite Chevalley groups. The subschemes obtained in this way could be considered as an association scheme version of Weyl groups for Chevalley groups.
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