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.

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DOI: 10.5802/alco.148
Classification: 05E05, 20C08, 14M15
Keywords: Schubert polynomials, Grothendieck polynomials, Coxeter systems, reduced words.
Marberg, Eric 1; Pawlowski, Brendan 2

1 Hong Kong University of Science and Technology Department of Mathematics Clear Water Bay, Hong Kong
2 University of Southern California Los Angeles, California, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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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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