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.
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Mots clés : 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 = {http://www.numdam.org/articles/10.5802/alco.148/}
}
TY - JOUR AU - Marberg, Eric AU - Pawlowski, Brendan TI - Principal specializations of Schubert polynomials in classical types JO - Algebraic Combinatorics PY - 2021 SP - 273 EP - 287 VL - 4 IS - 2 PB - MathOA foundation UR - http://www.numdam.org/articles/10.5802/alco.148/ DO - 10.5802/alco.148 LA - en ID - ALCO_2021__4_2_273_0 ER -
%0 Journal Article %A Marberg, Eric %A Pawlowski, Brendan %T Principal specializations of Schubert polynomials in classical types %J Algebraic Combinatorics %D 2021 %P 273-287 %V 4 %N 2 %I MathOA foundation %U http://www.numdam.org/articles/10.5802/alco.148/ %R 10.5802/alco.148 %G en %F ALCO_2021__4_2_273_0
Marberg, Eric; Pawlowski, Brendan. Principal specializations of Schubert polynomials in classical types. Algebraic Combinatorics, Tome 4 (2021) no. 2, pp. 273-287. doi : 10.5802/alco.148. http://www.numdam.org/articles/10.5802/alco.148/
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