2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112922We 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.22 pages, LaTeXRepresentation TheoryAlgebraic Geometrytext