Principal specializations of Schubert polynomials in classical types
Abstract
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.
Keywords
Cite
@article{arxiv.2002.00303,
title = {Principal specializations of Schubert polynomials in classical types},
author = {Eric Marberg and Brendan Pawlowski},
journal= {arXiv preprint arXiv:2002.00303},
year = {2022}
}
Comments
17 pages; v2: added several examples to the introduction, updated references; v3: fixed typos in Theorem 1.11 and Example 1.12, final version