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Mathematical Research Letters
Volume 27 (2020)
Number 3
On the affine Schützenberger involution
Pages: 809 – 834
DOI: https://dx.doi.org/10.4310/MRL.2020.v27.n3.a9
Author
Abstract
We consider an involution on the affine Weyl group of type $A$ 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 $A$ evaluated at $-1$.
Received 29 December 2018
Accepted 22 July 2019
Published 20 August 2020