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arXiv · 1608.02447

Shifted symmetric functions and multirectangular coordinates of Young diagrams

Per Alexandersson·Valentin Féray
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Abstract

In this paper, we study shifted Schur functions $S_\mu^\star$, as well as a new family of shifted symmetric functions $\mathfrak{K}_\mu$ linked to Kostka numbers. We prove that both are polynomials in multi-rectangular coordinates, with nonnegative coefficients when written in terms of falling factorials. We then propose a conjectural generalization to the Jack setting. This conjecture is a lifting of Knop and Sahi's positivity result for usual Jack polynomials and resembles recent conjectures of Lassalle. We prove our conjecture for one-part partitions.

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Per Alexandersson, Valentin Féray. 2016-08-08. Shifted symmetric functions and multirectangular coordinates of Young diagrams. https://doi.org/10.1016/j.jalgebra.2017.03.036

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