"Hyperplane arrangements and diagonal harmonics"

Drew Armstrong
University of Miami

Monday, November 9, 2009
4:00 pm, 845 Patterson Office Tower

Abstract:

We will define two statistics --- one old and one new --- on the chambers of a Shi hyperplane arrangement. We show that the joint distribution of these on the dominant Shi chambers is the q,t-Catalan number and we conjecture that the joint distribution on all chambers is the Hilbert series of the diagonal harmonics. We show (via a bijection with labeled lattice paths) that our conjecture is equivalent to a conjecture of Haglund and Loehr.