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

Mitya Boyarchenko; Maria Sabitova

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

Mitya Boyarchenko·Maria Sabitova

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Abstract

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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BibTeX RIS

Mitya Boyarchenko, Maria Sabitova. 2006-05-26. Centralizers of generic elements of Newton strata in the adjoint quotients of reductive groups. https://arxiv.org/abs/math/0605693

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