  We study the Newton stratification of the adjoint quotient of a connected
split reductive group G with simply connected derived group over the field F of
formal Laurent series in one variable over the field of complex numbers. Our
main result describes the centralizer of a regular semisimple element in G(F)
whose image in the adjoint quotient lies in a certain generic subset of a given
Newton stratum. Other noteworthy results include analogues of some results of
Springer on regular elements of finite reflection groups, as well as a
geometric construction of a well known homomorphism from the fundamental group
of a reduced and irreducible root system to the Weyl group of the system.
