Discrete CATS Seminar
U N I V E R S I T Y
K E N T U C K Y
WHERE CATS =
845 PATTERSON OFFICE TOWER
"Hyperplane arrangements and diagonal harmonics"
University of Miami
Monday, November 9, 2009
4:00 pm, 845 Patterson Office Tower
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.