@article{2c23d5333f5645479b8354c6ab1dec3a,
title = "Multiplicity-Free Key Polynomials",
abstract = "The key polynomials, defined by Lascoux–Sch{\"u}tzenberger, are characters for the Demazure modules of type A. We classify multiplicity-free key polynomials. The proof uses two combinatorial models for key polynomials. The first is due to Kohnert. The second is in terms of Searles{\textquoteright} rule for the quasi-key polynomials of Assaf–Searles. Our argument proves a sufficient condition for a quasi-key polynomial to be multiplicity-free.",
author = "Reuven Hodges and Alexander Yong",
note = "Funding Information: We thank Mahir Can for helpful communications. We thank David Brewster and Husnain Raza for writing computer code (as part of their NSF RTG funded ICLUE program) that was useful for checking parts of the proof. We used the Maple packages ACE and Coxeter/Weyl in our investigations. AY was partially supported by a Simons Collaboration Grant, and an NSF RTG grant. RH was partially supported by an AMS-Simons Travel Grant. Funding Information: We thank Mahir Can for helpful communications. We thank David Brewster and Husnain Raza for writing computer code (as part of their NSF RTG funded ICLUE program) that was useful for checking parts of the proof. We used the Maple packages ACE and Coxeter/Weyl in our investigations. AY was partially supported by a Simons Collaboration Grant, and an NSF RTG grant. RH was partially supported by an AMS-Simons Travel Grant. Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",
year = "2023",
month = jun,
doi = "10.1007/s00026-022-00574-7",
language = "English (US)",
volume = "27",
pages = "387--411",
journal = "Annals of Combinatorics",
issn = "0218-0006",
publisher = "Birkhauser Verlag Basel",
number = "2",
}