# The McKay correspondence via tilting

## Morgan Brown (Michigan)

Let $G$ be a subgroup of $SL_n(\mathbb{C})$. When $n=2$, $\mathbb{C}^n/G$ has a unique minimal resolution, and the classical McKay correspondence relates the representation theory of $G$ with the structure of this resolution. For $n=3$, Bridgeland, King, and Reid used categorical techniques to show that $\mathbb{C}^n/G$ has a distinguished crepant resolution Y=$G$-Hilb. Specifically, they showed that there is an equivalence between the derived categories $D^G(\mathbb{C}^n) and $D(Y)$. I will show how one can use this equivalence to describe the coherent sheaves on $Y$ in terms of $G$-equivariant objects on $X$ by a process called tilting. This is joint work with Ian Shipman.

Tuesday, April 2nd, at 4:00pm in HBH 227

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