Gröbner geometry of Schubert polynomials through ice

The geometric naturality of Schubert polynomials and their combinatorial pipe dream representations was established by Knutson and Miller (2005) via antidiagonal Gröbner degeneration of matrix Schubert varieties. We consider instead diagonal Gröbner degenerations. In this dual setting, Knutson, Mill...

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Bibliographic Details
Published inAdvances in mathematics (New York. 1965) Vol. 398; p. 108228
Main Authors Hamaker, Zachary, Pechenik, Oliver, Weigandt, Anna
Format Journal Article
LanguageEnglish
Published Elsevier Inc 26.03.2022
Subjects
Bumpless pipe dream
Gröbner bases
Matrix Schubert variety
Schubert polynomial
Gröbner bases
Matrix Schubert variety
Bumpless pipe dream
Schubert polynomial
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Summary:The geometric naturality of Schubert polynomials and their combinatorial pipe dream representations was established by Knutson and Miller (2005) via antidiagonal Gröbner degeneration of matrix Schubert varieties. We consider instead diagonal Gröbner degenerations. In this dual setting, Knutson, Miller, and Yong (2009) obtained alternative combinatonarics for the class of “vexillary” matrix Schubert varieties. We initiate a study of general diagonal degenerations, relating them to a neglected formula of Lascoux (2002) in terms of the 6-vertex ice model (recently rediscovered by Lam, Lee, and Shimozono (2021) in the guise of “bumpless pipe dreams”).
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2022.108228