Metacommutation of primes in Eichler orders
Volume 197 / 2021
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.
