Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:****Drew Sills**, Rutgers University, asills {at} math [dot] rutgers [dot] edu**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

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

Abstract:

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.