Séminaire Lotharingien de Combinatoire, 82B.31 (2019), 12 pp.

Sami Assaf and Dominic Searles

Skew polynomials and extended Schur functions

Abstract. Using Kohnert's algorithm, we associate a polynomial to any cell diagram in the positive quadrant, simultaneously generalizing Schubert polynomials and GLn Demazure characters. We survey properties of these Kohnert polynomials and their stable limits, which are quasisymmetric functions. As a first application, we introduce and study two new bases of Kohnert polynomials, one of which stabilizes to the skew-Schur functions and is conjecturally Schubert-positive, the other stabilizes to a new basis of quasisymmetric functions that contains the Schur functions.

Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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