**Next:**Luc Lapointe - To

**Up:**Algebraic Combinatorics, Group Representations

**Previous:**Victor Ginzburg - Principal

##
Mark Haiman - *The McKay correspondence and the **n*! conjecture

*n*! conjecture

MARK HAIMAN, University of California at San Diego, La Jolla, California 92093-0112, USA |

The McKay correspondence and the n! conjecture |

The McKay correspondence is a remarkable conjecture
asserting that if *G* is a finite group of linear endomorphisms with
determinatn 1 of a complex vector space *V*, and *X* is a special type
(called *crepant*) of resolution of singularities of the orbit space
*V*/*G*, then the Betti numbers of *X* sum to the number of conjugacy
classes of *G*. As a step toward explaining the McKay correspondence,
Nakamura has proposed that a space known as the *G*-Hilbert scheme
should be a crepant resolution of *V*/*G* whenever one exists. When *G*is the symmetric group acting on the direct sum of two copies of its
natural representation, Nakamura's conjecture is equivalent to the
``*n*! conjecture'' of Garsia and myself.

**Next:**Luc Lapointe - To

**Up:**Algebraic Combinatorics, Group Representations

**Previous:**Victor Ginzburg - Principal