Specification: Weyl Group Elements (OSCAR v1.3)

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

In OSCAR v1.3, WeylGroupElem still uses a typed _type object, but its payload shape differs from OSCAR v1.2 before the surrounding WeylGroup encoding changes again in OSCAR v1.4.

Encoding Notes

• Use _type.name = "WeylGroupElem".
• Store the reduced word under data.
• Refer to the parent group according to the OSCAR v1.3 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", "1.3.1"]},
  "_type": {"name": "WeylGroupElem", "params": "84d2dfc7-8254-4a2c-be91-56d9f46bc8ae"},
  "data": ["1", "2", "3"],
  "_refs": {
    "84d2dfc7-8254-4a2c-be91-56d9f46bc8ae": {"_type": "WeylGroup", "data": {"root_system": "80e4d279-7dd2-4f5a-94bf-747460d2a2b4"}},
    "80e4d279-7dd2-4f5a-94bf-747460d2a2b4": {
      "_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