We review the combinatorial interpretations of Macdonald polynomial and diagonal harmonics, and some combinatorial formulas. From the geometric point of view, we know that the former is related to the fiber of an isopectral scheme over the Hilbert scheme, and the latter has connection to the Euler characteristic of the isopectral tensor the zero fiber closed subscheme. We will explain the fundamentals of these terms. Look at some example in small n cases, where we express the morphism in regular rings.
Graduate Student Combinatorics Seminar
Wednesday, March 24, 2010 - 12:30pm
Tian Liang
University of Pennsylvania