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Metacommutation of primes in Eichler orders

Volume 197 / 2021

Angelica Babei, Sara Chari Acta Arithmetica 197 (2021), 77-92 MSC: Primary 11S45; Secondary 11R52. DOI: 10.4064/aa191031-23-5 Published online: 31 August 2020

Abstract

We study the metacommutation problem in Eichler orders. From this arises a permutation of the set of locally principal left ideals of a given prime reduced norm. Previous results on the cycle structure were determined for locally maximal orders. As we extend these results, we present an alternative, combinatorial description of the metacommutation permutation as an action on the Bruhat–Tits tree.

Authors

  • Angelica BabeiStevenson Center
    Vanderbilt University
    Nashville, TN 37212, U.S.A.
    e-mail
  • Sara ChariHathorn Hall
    Bates College
    Lewiston, ME 04240, U.S.A.
    e-mail

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