Specification: Weyl Group Elements (OSCAR v1.2)

Profiles: OSCAR v1.2 Other versions: Weyl Group Elements (OSCAR v1.3), Weyl Group Elements (OSCAR v1.4-v1.8)

In OSCAR v1.2, WeylGroupElem already uses a typed _type object, but it refers to a WeylGroup encoded with the older bare-type representation.

Encoding Notes

• Use _type.name = "WeylGroupElem".
• Store the reduced word under data.
• Refer to the parent group according to the OSCAR v1.2 WeylGroup encoding.

Canonical Example Payload

The following payload is taken directly from the current rosetta-stone corpus.

{
  "_ns": {"Oscar": ["https://github.com/oscar-system/Oscar.jl", "1.2.2"]},
  "_type": {"name": "WeylGroupElem", "params": "a3d3fc87-58b7-49aa-b7a7-7832d64890d9"},
  "data": ["3", "1", "2"],
  "_refs": {
    "a3d3fc87-58b7-49aa-b7a7-7832d64890d9": {"_type": "WeylGroup", "data": {"root_system": "b484b455-557b-41fc-8e7a-97ba564c6b3a"}},
    "b484b455-557b-41fc-8e7a-97ba564c6b3a": {
      "_type": "RootSystem",
      "data": {
        "cartan_matrix": [
          ["2", "-1", "0", "0", "0", "0"],
          ["-1", "2", "0", "0", "0", "0"],
          ["0", "0", "2", "-1", "0", "0"],
          ["0", "0", "-1", "2", "-1", "0"],
          ["0", "0", "0", "-1", "2", "-1"],
          ["0", "0", "0", "0", "-2", "2"]
        ],
        "type": [["A", "2"], ["B", "4"]]
      }
    }
  }
}

Documented Profiles in This Corpus

This table records the profile/version pairs currently represented by the rosetta-stone examples for this data type. Add new rows as new systems or encoding revisions are documented.

Rosetta Stone Examples

• Element of Weyl group