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The McKay correspondence as an equivalence of derived categories
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Bridgeland, Tom, King, Alastair and Reid, Miles (2001) The McKay correspondence as an equivalence of derived categories. American Mathematical Society. Journal, Vol.14 (No.3). pp. 535-554. doi:10.1090/S0894-0347-01-00368-X ISSN 0894-0347.
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Official URL: http://dx.doi.org/10.1090/S0894-0347-01-00368-X
Abstract
The classical McKay correspondence relates representations of a finite subgroup
G ⊂ SL(2,C) to the cohomology of the well-known minimal resolution of the
Kleinian singularity C2/G. Gonzalez-Sprinberg and Verdier [10] interpreted the
McKay correspondence as an isomorphism on K theory, observing that the representation
ring of G is equal to the G-equivariant K theory of C2. More precisely,
they identify a basis of the K theory of the resolution consisting of the classes of
certain tautological sheaves associated to the irreducible representations of G.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Dynkin diagrams, Kleinian groups, Point set theory | ||||
Journal or Publication Title: | American Mathematical Society. Journal | ||||
Publisher: | American Mathematical Society | ||||
ISSN: | 0894-0347 | ||||
Official Date: | 2001 | ||||
Dates: |
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Volume: | Vol.14 | ||||
Number: | No.3 | ||||
Page Range: | pp. 535-554 | ||||
DOI: | 10.1090/S0894-0347-01-00368-X | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Funder: | International Centre for Theoretical Physics (Trieste), Engineering and Physical Sciences Research Council (EPSRC) |
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