
TL;DR
This paper introduces the concept of G-characters for finitely generated groups and demonstrates how their quotient by trace-preserving automorphisms relates to the variety of G-characters in specific cases.
Contribution
It defines the variety of G-characters and establishes its normalization via quotient by trace-preserving outer automorphisms for certain classes of groups.
Findings
The G-character variety is well-defined for finitely generated groups.
The quotient by trace-preserving automorphisms normalizes the G-character variety.
Results apply to free, free abelian, and surface groups.
Abstract
Let G be a connected reductive affine algebraic group. In this short note we define the "variety of G-characters" of a finitely generated group F and show that the quotient of the G-character variety of F by the action of the trace preserving outer automorphisms of G normalizes the variety of G-characters when F is a free group, free abelian group, or a surface group.
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