2006/05/26 by Mitya Boyarchenko, Boyarchenko, Mitya, Maria Sabitova +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT
paper · pdf · doi:10.48550/arxiv.math/0605693
22 pages, LaTeX
arxiv created 2006/05/26 · arxiv updated 2009/12/01
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.