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

Igor V. Dolgachev

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arXiv · 0710.2253

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

Igor V. Dolgachev

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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 finite-dimensional unitary representations of G and vector bundles on an open algebraic surface with the trivial canonical class canonically associated to G.

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BibTeX RIS

Igor V. Dolgachev. 2007-12-14. McKay's correspondence for cocompact discrete subgroups of SU(1,1). https://arxiv.org/abs/0710.2253

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