# ALGEBRAIC COMBINATORICS

Principal specializations of Schubert polynomials in classical types
Algebraic Combinatorics, Volume 4 (2021) no. 2, pp. 273-287.

There is a remarkable formula for the principal specialization of a type A Schubert polynomial as a weighted sum over reduced words. Taking appropriate limits transforms this to an identity for the backstable Schubert polynomials recently introduced by Lam, Lee, and Shimozono. This note identifies some analogues of the latter formula for principal specializations of Schubert polynomials in classical types B, C, and D. We also describe some more general identities for Grothendieck polynomials. As a related application, we derive a simple proof of a pipe dream formula for involution Grothendieck polynomials.

Revised:
Accepted:
Published online:
DOI: https://doi.org/10.5802/alco.148
Classification: 05E05,  20C08,  14M15
Keywords: Schubert polynomials, Grothendieck polynomials, Coxeter systems, reduced words.
@article{ALCO_2021__4_2_273_0,
author = {Marberg, Eric and Pawlowski, Brendan},
title = {Principal specializations of Schubert polynomials in classical types},
journal = {Algebraic Combinatorics},
pages = {273--287},
publisher = {MathOA foundation},
volume = {4},
number = {2},
year = {2021},
doi = {10.5802/alco.148},
language = {en},
url = {https://alco.centre-mersenne.org/articles/10.5802/alco.148/}
}
Marberg, Eric; Pawlowski, Brendan. Principal specializations of Schubert polynomials in classical types. Algebraic Combinatorics, Volume 4 (2021) no. 2, pp. 273-287. doi : 10.5802/alco.148. https://alco.centre-mersenne.org/articles/10.5802/alco.148/

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