Procesi Bundles and Symplectic Reflection Algebras

  • Ivan LosevEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 269)


In this survey we describe an interplay between Procesi bundles on symplectic resolutions of quotient singularities and Symplectic reflection algebras. Procesi bundles were constructed by Haiman and, in a greater generality, by Bezrukavnikov and Kaledin. Symplectic reflection algebras are deformations of skew-group algebras defined in complete generality by Etingof and Ginzburg. We construct and classify Procesi bundles, prove an isomorphism between spherical Symplectic reflection algebras, give a proof of wreath Macdonald positivity and of localization theorems for cyclotomic Rational Cherednik algebras.

MSC 2010

14E16 53D20 53D55 (Primary)05E05 16G20 16G99 16S36 17B63 20F55 (Secondary) 



This survey is a greatly expanded version of lectures I gave at Northwestern in May 2012. I would like to thank Roman Bezrukavnikov and Iain Gordon for numerous stimulating discussions. My work was supported by the NSF under Grant DMS-1161584.


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Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

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