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The role of compositions in symmetric function theory

Algebra & Discrete Mathematics

Speaker: Sarah Mason, UC-Berkeley
Location: 1147 MSB
Start time: 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.