Symplectic keys and Demazure atoms in type C
Combinatorics
2021-03-24 v3
Abstract
We compute, mimicking the Lascoux-Sch\"utzenberger type A combinatorial procedure, left and right keys for a Kashiwara-Nakashima tableau in type C. These symplectic keys have a similar role as the keys for semistandard Young tableaux. More precisely, our symplectic keys give a tableau criterion for the Bruhat order on the hyperoctahedral group and cosets, and describe Demazure atoms and characters in type C. The right and the left symplectic keys are related through the Lusztig involution. A type C Sch\"utzenberger evacuation is defined to realize that involution.
Keywords
Cite
@article{arxiv.1910.14115,
title = {Symplectic keys and Demazure atoms in type C},
author = {João Miguel Santos},
journal= {arXiv preprint arXiv:1910.14115},
year = {2021}
}
Comments
Accepted in Electronic Journal of Combinatorics. Some notation has changed. 26 pages