2015/01/04 by Losev, Ivan
#14E16 #16G20 #16G99 #16S36 #17B63 #20F55 (Secondary) #53D20 #53D55 (Primary) 05E05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.1501.00643
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.