Centralizers of generic elements of Newton strata in the adjoint quotients of reductive groups

Details Centralizers of generic elements of Newton strata in the adjoint quotients of reductive groups Centralizers of generic elements of Newton strata in the adjoint quotients of reductive groups

2006-05-26

arxiv.org/abs/math/0605693v1

Mathematics

Representation Theory

22 pages, LaTeX

Scientific paper

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.

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