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The McKay correspondence as an equivalence of derived categories

By Tom Bridgeland, Alastair King and Miles Reid

Abstract

The classical McKay correspondence relates representations of a finite subgroup\ud G ⊂ SL(2,C) to the cohomology of the well-known minimal resolution of the\ud Kleinian singularity C2/G. Gonzalez-Sprinberg and Verdier [10] interpreted the\ud McKay correspondence as an isomorphism on K theory, observing that the representation\ud ring of G is equal to the G-equivariant K theory of C2. More precisely,\ud they identify a basis of the K theory of the resolution consisting of the classes of\ud certain tautological sheaves associated to the irreducible representations of G

Topics: QA
Publisher: American Mathematical Society
Year: 2001
OAI identifier: oai:wrap.warwick.ac.uk:4297

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