# A Decomposition of Schur Functions and an Analogue of the Robinson-Schensted-Knuth Algorithm

Abstract. We exhibit a weight-preserving bijection between semi-standard Young tableaux and semi-skyline augmented fillings to provide a combinatorial proof that the Schur functions decompose into nonsymmetric functions indexed by compositions. The insertion procedure involved in the proof leads to an analogue of the Robinson-Schensted-Knuth Algorithm for semi-skyline augmented fillings. This procedure commutes with the Robinson-Schensted-Knuth Algorithm, and therefore retains many of its properties.

Received: February 9, 2007. Accepted: September 18, 2008. Final Version: September 18, 2008.

The following versions are available:

## Comment by Sarah Mason

Sarah Mason adds several remarks, clarifying that the nonsymmetric polynomials denoted Ê\alpha(X;q,t) in the paper are equivalent to Demazure characters, introduced by Demazure, and that the specialization of these polynomials studied in the paper has been investigated by Lascoux and Schü:tzenberger under the name of "standard bases" respectively "Demazure atoms." The relevant references are provided.