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 GL_n 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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