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arXiv · 2307.02473

Fixed elements of pircon automorphisms

Mikael Hansson·Vincent Umutabazi
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Abstract

We prove that the subposet induced by the fixed elements of any automorphism of a pircon is also a pircon. By a result of Abdallah, Hansson, and Hultman, the order complex of any open interval in a pircon is a PL ball or a PL sphere. We apply our main results to symmetric groups of the form $S_{2n}$. A consequence is that the fixed point free signed involutions form a pircon under the dual of the Bruhat order on the hyperoctahedral group. Finally, we prove that this poset is, in fact, EL-shellable, which is a type $B$ analogue of a result of Can, Cherniavsky, and Twelbeck.

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Mikael Hansson, Vincent Umutabazi. 2023-07-05. Fixed elements of pircon automorphisms. https://arxiv.org/abs/2307.02473

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