English

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 AA 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 AA 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

R2 v1 2026-06-23T01:24:46.106Z