\documentclass[ALCO,published]{cedram}

\Relation[corrige]{10.5802/alco.13}
\CDRsetmeta{articletype}{erratum}

\title{Corrigendum: A Demazure crystal construction for Schubert polynomials}  

\author{\firstname{Sami} \lastname{Assaf}}
\address{Department of Mathematics, University of Southern California, 3620 S. Vermont Ave., Los Angeles, CA 90089-2532, U.S.A.}
\email{shassaf@usc.edu}

\author{\firstname{Anne} \lastname{Schilling}}
\address{Department of Mathematics, UC Davis, One Shields Ave., Davis, CA 95616-8633, U.S.A.}
\email{anne@math.ucdavis.edu}

\subjclass{14N15, 05E10, 05A05, 05E05, 05E18, 20G42}

\keywords{Schubert polynomials, Demazure characters, Stanley symmetric functions, crystal bases}

\datepublished{2024-10-31}
\begin{document}

\begin{abstract}
We give a corrigendum to our paper~\cite{AS.2018} entitled ``A Demazure crystal construction for Schubert polynomials''.
\end{abstract}

\CDRGrant[NSF]{DMS-2053350}
\CDRGrant[NSF]{DMS-2246785}

\maketitle

\section{Introduction}
We provide a corrigendum to our paper~\cite{AS.2018}, which cites preprint~\cite{Ass-R} for various definitions and results
in~\cite[Section 5.2]{AS.2018}. 
Preprint~\cite{Ass-R} was withdrawn from the arXiv, hence we point here to the correct published citations for the definitions and results needed
in~\cite{AS.2018}.

\section{Reference pointers for \texorpdfstring{\cite[Section 5.2]{AS.2018}}{Section 5.2}}

\noindent
\textbf{Lift map:} The lift map in~\cite[Section 5.2]{AS.2018} needs to be replaced by the lift map in~\cite[Definition 4.22]{Ass-Rnew}.

\smallskip

\noindent
\textbf{Drop map:} The drop map in~\cite[Section 5.2]{AS.2018} needs to be replaced by the drop map in~\cite[Definition 4.9]{Ass-Rnew}.

\smallskip

\noindent
\textbf{Weak Edelman--Greene insertion:} 
\begin{itemize}
\item
The definition \cite[Definition 5.6]{AS.2018} should cite~\cite[Definition 5.6]{Ass-Rnew}. 
The property that the column sorting map $\phi$ satisfies $\phi(\hat{Q}(\rho))=Q(\rho)$, where $\rho$ is a reduced expression, $\hat{Q}$ is the 
recording tableau of weak Edelman--Greene insertion and $Q$ is the recording tableau of Edelman-Greene insertion follows 
from~\cite[Theorems 5.4 and 5.11]{Ass-Rnew}. The reference to~\cite[Theorem 3.24]{Ass-W} in the proof of~\cite[Theorem 5.11]{Ass-Rnew} should 
be~\cite[Theorem 2.21]{Ass-W}.
\item
The result~\cite[Theorem 5.7]{AS.2018} is~\cite[Corollary 5.12]{Ass-Rnew}. 
\item
The citation~\cite[Theorem 2.4]{Ass-R} in the proof of~\cite[Corollary 5.8]{AS.2018} is~\cite[Proposition~2.6]{Ass-Rnew}.
\item
The result \cite[Corollary 5.9]{AS.2018} is~\cite[Corollary 4.24]{Ass-Rnew}.
\end{itemize}


\longthanks{
AS was partially supported by NSF grant DMS-2053350. SA was partially supported by NSF grant DMS-2246785.

The authors are grateful to Eric Marberg and Elizabeth Milicevic for their comments.
}

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