Quasiparabolic sets and Stanley symmetric functions for affine fixed-point-free involutions

[摘要] We introduce and study affine analogues of the fixed-point-free (FPF) involution Stanley symmetric functions of Hamaker, Marberg, and Pawlowski. Our methods use the theory of quasiparabolic sets introduced by Rains and Vazirani, and we prove that the subset of FPF-involutions is a quasiparabolic set for the affine symmetric group under conjugation. Using properties of quasiparabolic sets, we prove a transition formula for the affine FPF involution Stanley symmetric functions, analogous to Lascoux and Schutzenberger's transition formula for Schubert polynomials. Our results suggest several conjectures and open problems. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-12-01

[关键词] Affine symmetric groups;Stanley symmetric functions;Quasiparabolic sets;Bruhat order