On the affine Schützenberger involution
arXiv:1804.05636
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.
18 pages; v2, v3: minor correction