Mark Haiman

Abstract:   It has occurred to a number of people that the geometry surrounding Macdonald polynomials, the Hilbert scheme, and the "n!" theorem should have generalizations to groups other than the symmetric group. One candidate is a Weyl group acting on two copies of its natural representation, but it seems necessary restrict the problem in order to extend the program in that direction.

I propose instead to consider the wreath product of the symmetric group with a finite subgroup G of SL(2), replacing the Hilbert scheme with a quiver variety corresponding to the fundamental affine weight. It requires care to identify the correct conjecture in this context, but I have a good candidate and some theoretical and computational evidence to to support it.

When G=Z/2Z, there are natural choices of quiver variety giving theories of types B_n and C_n. More generally when G=Z/rZ, the picture leads to new conjectures analogous to the Macdonald positivity theorem, which now have strong computational support.

Here are some directions to Northeastern University. Lake Hall and Nightingale Hall can be best accessed from the entrance on the corner of Greenleaf Street and Leon Street. The two halls are connected, with no well-defined boundary in between. In particular, 509 Lake Hall is on the same corridor as 544 Nightingale Hall.

There is free parking available for people coming to the Colloquium at Northeastern's visitor parking (Rennaisance Garage). The entrance is from Columbus Avenue. If coming by car, you should park there and take the parking talon. After the lecture, you may pick up the payment coupon from Maxim Braverman.