The role of compositions in symmetric function theoryAlgebra & Discrete Mathematics
|Sarah Mason, UC-Berkeley
|Fri, Dec 1 2006, 12:10PM
The Schur functions form a symmetric function basis with many applications to combinatorics and representation theory. They can be decomposed into smaller functions which are indexed by compositions. These functions, called nonsymmetric Schur functions, are described combinatorially using Haglund, Haiman, and Loehr's results on nonsymmetric Macdonald polynomials. We demonstrate several key properties of the nonsymmetric Schur functions, including an analogue of the Robinson-Schensted-Knuth Algorithm and a connection to Demazure characters.