Splitting fields of association schemes

The splitting field K of a commutative association scheme is the extension of the rationals by the adjunction of all eigenvalues of the association scheme. Let L be a subfield of K containing all the Krein parameters. It is shown that the Galois group of K L is contained in the center of the Galois group of K Q. In particular, if the Krein parameters are all rational, then the eigenvalues are contained in a cyclotomic number field.