Dimension des fibres de Springer affines pour les groupes

TL;DR

This paper develops a new framework for analyzing affine Springer fibers for groups by constructing an adjoint quotient and a regular centralizer, building on Steinberg and Ngô's work.

Contribution

It introduces a novel approach to compute affine Springer fibers using the Vinberg semi-group and regular centralizers, extending previous theories.

Findings

Construction of an adjoint quotient for the Vinberg semi-group

Existence of a regular centralizer on the quotient

Explicit computation of affine Springer fibers for groups

Abstract

Following Steinberg, we construct an adjoint quotient for the Vinberg semi-group and a section to this quotient. Then, after Ng\^o, we show the existence of a regular centralizer on it and use it to compute the affine Springer fibers for groups.