On the affine Sch\"utzenberger involution
Representation Theory
2018-10-09 v3 Combinatorics
Abstract
We consider an involution on the affine Weyl group of type induced from the nontrivial automorphism on the (finite) Dynkin diagram. We prove that the number of left cells fixed by this involution in each two-sided cell is given by a certain Green polynomial of type evaluated at -1.
Keywords
Cite
@article{arxiv.1804.05636,
title = {On the affine Sch\"utzenberger involution},
author = {Dongkwan Kim},
journal= {arXiv preprint arXiv:1804.05636},
year = {2018}
}
Comments
18 pages; v2, v3: minor correction