McKay's correspondence for cocompact discrete subgroups of SU(1,1)
Abstract
The classical McKay correspondence establishes an explicit link from the representation theory of a finite subgroup G of SU(2) and the geometry of the minimal resolution of the quotient of the affine plane by G. In this paper we discuss a possible generalization of the McKay correspondence to the case when G is replaced with a cocompact discrete subgroup of the universal cover of SU(1,1) such that its image in PSU(1,1) is a cocompact fuchsian group with quotient of genus 0. We establish a correspondence between a certain class of finitedimensional unitary representations of G and vector bundles on an open algebraic surface with the trivial canonical class canonically associated to G.
 Publication:

arXiv eprints
 Pub Date:
 October 2007
 arXiv:
 arXiv:0710.2253
 Bibcode:
 2007arXiv0710.2253D
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Geometric Topology
 EPrint:
 Essentially revised version with added bibliography