KEY POLYNOMIALS AND A FLAGGED LITTLEWOOD-RICHARDSON RULE

This paper studies a family of polynomials called key polynomials, int roduced by Demazure and investigated combinatorially by Lascoux and Sc hutzenberger. We give two new combinatorial interpretations for these key polynomials and show how they provide the connection between two r elatively recent combinatorial expressions for Schubert polynomials. W e also give a flagged Littlewood-Richardson rule, an expansion of a fl agged skew Schur function as a nonnegative sum of key polynomials. (C) 1995 Academic Press, Inc.