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 RSK algorithm, and therefore retains many of its properties.

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

Cited by in corpus (5)

• Set-Valued Skyline Fillings
• Row-strict Quasisymmetric Schur Functions, Characterizations of Demazure Atoms, and Permuted Basement Nonsymmetric Macdonald Polynomials
• NW-SE expansions of non-symmetric Cauchy kernels on near staircases and growth diagrams
• Backward jeu de taquin slides for composition tableaux and a noncommutative Pieri rule
• Skew row-strict quasisymmetric Schur functions