2015-07-01Tesler Matrices and Diagonal HarmonicsJames Haglund (University of Pennsylvania)
The study of the (bigheaded) character of Diagonal Harmonics is a well-known topic in algebraic combinatorics and algebraic geometry initiated in the early 1990's by Garsia and Haiman. The topic has close connections to the study of Macdonald polynomials, which are symmetric functions with two extra parameters q, t. Haiman proved an expression for the character in terms of Macdonald polynomials using the Hilbert scheme. In this talk we discuss some recent formulas for the character, expressed in terms of simple objects known as Tesler matrices. Several open problems are highlighted.