A Decomposition of Schur functions and an analogue of the Robinson-Schensted-Knuth Algorithm

Details A Decomposition of Schur functions and an analogue of the Robinson-Schensted-Knuth Algorithm A Decomposition of Schur functions and an analogue of the Robinson-Schensted-Knuth Algorithm

2006-04-19

arxiv.org/abs/math/0604430v4

S\'eminaire Lotharingien de Combinatoire, 60 (2008), Art. B57e, 24pp

Mathematics

Combinatorics

24 pages; restructured; see journal for comment on connections to Demazure characters

Scientific paper

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 RSK algorithm, and therefore retains many of its properties.

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