Derivatives of Schubert polynomials and proof of a determinant conjecture of Stanley

Zachary Hamaker; Oliver Pechenik; David E. Speyer; Anna Weigandt

doi:10.5802/alco.93

Derivatives of Schubert polynomials and proof of a determinant conjecture of Stanley

Zachary Hamaker, Oliver Pechenik, David E. Speyer, Anna Weigandt

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We study the action of a differential operator on Schubert polynomials. Using this action, we first give a short new proof of an identity of I. Macdonald (1991). We then prove a determinant conjecture of R. Stanley (2017). This conjecture implies the (strong) Sperner property for the weak order on the symmetric group, a property recently established by C. Gaetz and Y. Gao (2019).

Original language	English (US)
Pages (from-to)	301-307
Number of pages	7
Journal	Algebraic Combinatorics
Volume	3
Issue number	2
DOIs	https://doi.org/10.5802/alco.93
State	Published - 2020
Externally published	Yes

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© 2020 Centre Mersenne NORMAL. All rights reserved.

Keywords

MacDonald identity
Schubert polynomial
Sperner property
Weak order

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10.5802/alco.93

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abstract = "We study the action of a differential operator on Schubert polynomials. Using this action, we first give a short new proof of an identity of I. Macdonald (1991). We then prove a determinant conjecture of R. Stanley (2017). This conjecture implies the (strong) Sperner property for the weak order on the symmetric group, a property recently established by C. Gaetz and Y. Gao (2019).",

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AU - Hamaker, Zachary

AU - Pechenik, Oliver

AU - Speyer, David E.

AU - Weigandt, Anna

PY - 2020

Y1 - 2020

N2 - We study the action of a differential operator on Schubert polynomials. Using this action, we first give a short new proof of an identity of I. Macdonald (1991). We then prove a determinant conjecture of R. Stanley (2017). This conjecture implies the (strong) Sperner property for the weak order on the symmetric group, a property recently established by C. Gaetz and Y. Gao (2019).

AB - We study the action of a differential operator on Schubert polynomials. Using this action, we first give a short new proof of an identity of I. Macdonald (1991). We then prove a determinant conjecture of R. Stanley (2017). This conjecture implies the (strong) Sperner property for the weak order on the symmetric group, a property recently established by C. Gaetz and Y. Gao (2019).

KW - MacDonald identity

KW - Schubert polynomial

KW - Sperner property

KW - Weak order

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DO - 10.5802/alco.93

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JO - Algebraic Combinatorics

JF - Algebraic Combinatorics

IS - 2

ER -

Derivatives of Schubert polynomials and proof of a determinant conjecture of Stanley

Abstract

Bibliographical note

Keywords

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