Sarah Mason
Published 2006-04-19, updated 2009-04-02Version 4
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.
Comments: 24 pages; restructured; see journal for comment on connections to Demazure characters
Journal: S\'eminaire Lotharingien de Combinatoire, 60 (2008), Art. B57e, 24pp
Decomposition of tensor products of Demazure crystals
The decomposition of 0-Hecke modules associated to quasisymmetric Schur functions
A combinatorial model for the decomposition of multivariate polynomials rings as an $S_n$-module
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