Quasiparabolic sets and Stanley symmetric functions for affine fixed-point-free involutions
Combinatorics
2019-11-15 v1 Representation Theory
Abstract
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 Sch\"utzenberger's transition formula for Schubert polynomials. Our results suggest several conjectures and open problems.
Keywords
Cite
@article{arxiv.1911.05961,
title = {Quasiparabolic sets and Stanley symmetric functions for affine fixed-point-free involutions},
author = {Yifeng Zhang},
journal= {arXiv preprint arXiv:1911.05961},
year = {2019}
}
Comments
23 pages