Derived Reid's recipe for abelian subgroups of SL3(C)

Timothy Logvinenko, October 29th, 2013

The classical McKay correspondence is a 1-1 correspondence between non-trivial
irreducible representations of a finite subgroup G of SL2(C) and irreducible divisors on the
minimal resolution Y of C2/G.

In this talk I describe joint work with Sabin Cautis and Alastair Craw in which we
generalize this correspondence to dimension three using the famous
Bridgeland-King-Reid derived equivalence. Specifically, we show that one can naturally
extract from this equivalence a correspondence between irreducible representations of
subrgroups G of SL3(C) and exceptional subvarieties of Y = G-Hilb(C3). The same
method applied to subgroups G of SL2(C) produces the classical McKay.