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SageMath: Root system data for type G
SageMath developers
Use in this reference: Linked primary source. Original algorithms and explanatory prose; no upstream software or document text is redistributed.
Relevant material: AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long.
Dependent assertions
| Record | Assertion | Source locator |
|---|---|---|
| G2 · (1,0) | Definition | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (1,0) | Complex dimension | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (1,0) | Coefficient field | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (1,0) | Quadratic Casimir C₂ | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (1,0) | Quadratic index T(R) | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (1,0) | Reality type | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (1,0) | Conjugate highest weight | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (1,0) | Descends to the adjoint global form | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (1,0) | Order of central kernel | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (1,0) | Highest weight and conventions | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (1,0) | Global form and center | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (1,0) | Use in a calculation | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (1,0) | Representation domain | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (0,1) | Definition | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (0,1) | Complex dimension | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (0,1) | Coefficient field | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (0,1) | Quadratic Casimir C₂ | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (0,1) | Quadratic index T(R) | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (0,1) | Reality type | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (0,1) | Conjugate highest weight | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (0,1) | Descends to the adjoint global form | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (0,1) | Order of central kernel | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (0,1) | Highest weight and conventions | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (0,1) | Global form and center | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (0,1) | Use in a calculation | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |
| G2 · (0,1) | Representation domain | AmbientSpace.simple_root(), fundamental_weights(): node 1 short and node 2 long. |