Weyl groups (experimental features)
This page is an addition to the documentation of Weyl groups with the additional experimental features.
Conversion to other group types
For many computations, it may be suitable to have a WeylGroup as a different kind of group object, to e.g. use functionality that is only available for that other type.
The conversion functions come in pairs: one only creates an isomorphic group object, the other also computes the isomorphism.
fp_group — Methodfp_group(W::WeylGroup) -> FPGroupConstruct a group of type FPGroup that is isomorphic to W.
The FPGroup will be the quotient of a free group with the same rank as W, where we have the natural 1-to-1 correspondence of generators, modulo the Coxeter relations of W.
Also see: isomorphism(::Type{FPGroup}, ::WeylGroup).
This function is part of the experimental code in Oscar. Please read here for more details.
isomorphism — Methodisomorphism(::Type{FPGroup}, W::WeylGroup) -> Map{WeylGroup, FPGroup}Construct an isomorphism between W and a group of type FPGroup.
The properties of the codomain group and the isomorphism are described in fp_group(::WeylGroup).
This function is part of the experimental code in Oscar. Please read here for more details.