Embeddings of root systems II: Permutation root systems

This paper studies a class of embeddings of “permutation” root systems, with properties abstracting those of examples of embeddings of linear root systems over commutative rings, as considered in the first paper in this series. The root system of one Coxeter group W (regarded as a permutation representation) is realized with its roots as sets of roots of another Coxeter group W′, with action induced by an embedding of W in (a completion of) W′.