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arXiv · 1804.05636

On the affine Sch\"utzenberger involution

Dongkwan Kim
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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.

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Dongkwan Kim. 2018-04-16. On the affine Sch\"utzenberger involution. https://arxiv.org/abs/1804.05636

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