Character Varieties

  title={Character Varieties},
  author={Adam S. Sikora},
Let G be a complex reductive algebraic group and let Γ be a finitely generated group. In this paper we study properties of irreducible and completely reducible representations ρ : Γ → G in the context of the geometric invariant theory of the G-action on Hom(Γ, G) by conjugation. In particular, we prove that ρ is poly-stable (i.e. its orbit is closed) if and only if ρ is completely reducible. We also show that ρ is properly stable (with respect to G/C(G)-action) if and only if ρ is irreducible… CONTINUE READING

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