Abstract
We define association schemes of affine type. These are the association schemes defined by the action of the semidirect products of finite classical groups and the underlying vector spaces on the same vector spaces. We show that the entries in the character tables of association schemes of affine type are expressed in terms of Gaussian periods. Furthermore, we show that the characer tables of association schemes of affine type defined by higher-dimensional classical groups are controlled by the character tables of association schemes of affine type defined by a lower-dimensional classical group.
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