主 题: The q,t-Catalan numbers and the space of Diagonal Harmonics
报告人: Prof. Jim Haglund (University of Pennsylvania)
时 间: 2007-07-06 下午 4:00 - 5:00
地 点: 理科一号楼 1490
We discuss the contents of a recent book of this title by the
author (which for the moment can be downloaded for free from
www.math.upenn.edu/~jhaglund).
We start by introducing the q,t-Catalan polynomial, studied by
the speaker, Loehr and others. We then discuss a generalization,
the q,t-Schroder polynomial, studied by Song, Egge and others.
Both of these are polynomials in two parameters, q and t, and
have purely combinatorial descriptions in terms of lattice paths.
We show how this work led to a conjecture for the character of
diagonal harmonics. Finally, we indicate how this in turn led to
a combinatorial formula for Macdonald polynomials, proved by
Haiman, Loehr and the speaker.
