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The classical McKay correspondence establishes an explicit link from therepresentation theory of a finite subgroup G of SU(2) and the geometry of theminimal resolution of the quotient of the affine plane by G. In this paper wediscuss a possible generalization of the McKay correspondence to the case whenG is replaced with a cocompact discrete subgroup of the universal cover ofSU(1,1) such that its image in PSU(1,1) is a cocompact fuchsian group withquotient of genus 0. We establish a correspondence between a certain class offinite-dimensional unitary representations of G and vector bundles on an openalgebraic surface with the trivial canonical class canonically associated to G.

McKay's correspondence for cocompact discrete subgroups of SU(1,1)