Let $k$ and $m$ be positive integers and $\lambda/\mu$ a skew partition. We compute the principal specialization of the skew Schur polynomials $s_{\lambda /\mu}(x_1, \ldots, x_{k})$ modulo $q^m-1$ under suitable conditions. We interpret the results thus obtained from the viewpoint of the cyclic sieving phenomenon on semistandard Young skew tableaux of shape $\lambda/\mu$. As an application, we deal with evaluations of the principal specialization of the skew Schur polynomials at roots of unity.
@article{10_37236_10941,
author = {So-Yeon Lee and Young-Tak Oh},
title = {Skew {Schur} polynomials and cyclic sieving phenomenon},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {4},
doi = {10.37236/10941},
zbl = {1503.05130},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10941/}
}
TY - JOUR
AU - So-Yeon Lee
AU - Young-Tak Oh
TI - Skew Schur polynomials and cyclic sieving phenomenon
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/10941/
DO - 10.37236/10941
ID - 10_37236_10941
ER -
%0 Journal Article
%A So-Yeon Lee
%A Young-Tak Oh
%T Skew Schur polynomials and cyclic sieving phenomenon
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/10941/
%R 10.37236/10941
%F 10_37236_10941
So-Yeon Lee; Young-Tak Oh. Skew Schur polynomials and cyclic sieving phenomenon. The electronic journal of combinatorics, Tome 29 (2022) no. 4. doi: 10.37236/10941
