For a faithful ZG lattice A and a field K on which the group G acts by field automorphisms, let R be the normal subgroup generated by the elements of G which act trivially on K and act as reflections on A. We prove that the rationality of the multiplicative invariant field K(A)(G) over K(A(R))(G) is equivalent to the rationality of K(A)(OmegaG) over K(A(R))(Omegag) where Omega (G) is a particular subgroup of G such that G/R congruent to Omega (G) . We then use this reduction result to prove that K(A)(G) is rational over K where G is the automorphism group of a crystallographic root system Psi, G acts trivially on K and A is any lattice on the space Q Psi. (C) 2001 Academic Press. [References: 18]
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