The GL(2, C) McKay correspondence

Wemyss, M. (2011) The GL(2, C) McKay correspondence. Mathematische Annalen, 350(3), pp. 631-659. (doi: 10.1007/s00208-010-0572-9)

Abstract

In this paper we show that for any affine complete rational surface singularity the quiver of the reconstruction algebra can be determined combinatorially from the dual graph of the minimal resolution. As a consequence the derived category of the minimal resolution is equivalent to the derived category of an algebra whose quiver is determined by the dual graph. Also, for any finite subgroup G of GL(2,C)GL(2,C), it means that the endomorphism ring of the special CM CC [[x, y]]G-modules can be used to build the dual graph of the minimal resolution of C2/GC2/G, extending McKay’s observation (McKay, Proc Symp Pure Math, 37:183–186, 1980) for finite subgroups of SL(2,C)SL(2,C) to all finite subgroups of GL(2,C)GL(2,C).

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Wemyss, Professor Michael
• Authors: Wemyss, M.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Mathematische Annalen
• Publisher: Springer-Verlag
• ISSN: 0025-5831
• ISSN (Online): 1432-1807
• Published Online: 07 September 2010
• Copyright Holders: Copyright © 2010 Springer-Verlag
• First Published: First published in Mathematische Annalen 350(3):631-659
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher