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Metacommutation of primes in Eichler orders
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Metacommutation of primes in Eichler orders
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In this article, we study the metacommutation problem in locally 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.
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Cited by 1 Pith paper
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Conjugation invariants determine the metacommutation permutation only up to relabelling
Conjugation-invariant data can determine the cycle shape of the metacommutation permutation, but never the labelled permutation, and not even a single destination, as shown by four indistinguishable primes with four d...
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