Tittel: McKay correspondence

Veileder: Louis-Philippe Thibault

Sammendrag: The goal of this thesis is to establish a 1-1 correspondence between quivers created from the four following sets whenever S is the power series ring $\mathbb{C}[[x, y]]$ and $G$ is a finite subgroup of $SL(2, \mathbb{C})$ acting on $S$.

  • The Maximal Cohen-Macaulay modules of the fixed ring $S^G$;
  • The indecomposable projective modules of the skew group algebra $S\# G$;
  • The indecomposable projective modules of $End_{S^G}(S)$;
  • The irreducible representations of $G$ (indecomposable $\mathbb{C}G$-modules).

Much of the thesis will be used to define these four quivers and to develop tools to establish such a correspondence.