Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)
Title: A Combinatorial Formula for Nonsymmetric Macdonald Polynomials
Speaker: Jim Haglund, University of Pennsylvania
Date: Thursday, November 16, 2006 5:00pm
Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ
Nonsymmetric Macdonald polynomials are multivariate polynomials which satisfy an orthogonality condition. They were introduced by Macdonald, after which Cherednik, Knop, Sahi and others developed the theory further. In this talk I will discuss how these functions form natural counterparts in many ways to the more well-known symmetric Macdonald polynomials. Then I will show how combinatorial results of a few years ago, joint with M. Haiman and N. Loehr, on the symmetric Macdonald polynomials, together with past results of Knop and Sahi on nonsymmetric Jack polynomials, led experimentally to a conjectured combinatorial formula for nonsymmetric poloynomials, which Haiman, Loehr and I have since proved.