#####
Séminaire Lotharingien de Combinatoire, B57e (2008), 24 pp.

# Sarah Mason

# 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.