WeylGroupExponents
The exponents of the Weyl group of the type: one less than each degree.
WeylGroupExponents(cartanType)The exponents of the Weyl group of the type: one less than each degree.Typed signatures
| Type | Package | Applies |
|---|---|---|
(cartan_type) -> list<integer> | combinatorics | always |
Details
- Defined over
CartanTypeas an expression in_x, evaluated by compute-engine — the definition IS the implementation. - Takes a
CartanTypeand nothing else — it reads values against their positions, or walks the orbits, so it needs the bijection. Applying it to a bare list is a type error, not a wrong answer.
Definition
Epsil, as the implementation runs it.
on CartanType, over _x
Apply(
(ds: list<integer>) => Apply((xs_init: list<integer>) => Fold(
(
xs: list<integer>,
x,
) => Apply(
(xs_next: list<integer>) => xs_next,
Join(xs, [x - 1]),
),
xs_init,
ds,
), []),
Range(2, _x[2] + 1, 1) if _x[1] == "A" else Map(
Function(2i, i),
Range(1, _x[2]),
) if _x[1] == "B" else Map(
Function(2i, i),
Range(1, _x[2]),
) if _x[1] == "C" else Join(
Filter(
Map(Function(2i, i), Range(1, _x[2] - 1)),
Function(e < _x[2], e),
),
[_x[2]],
Filter(
Map(Function(2i, i), Range(1, _x[2] - 1)),
Function(e >= _x[2], e),
),
) if _x[1] == "D" else ([2, 5, 6, 8, 9, 12] if _x[2] == 6 else [2, 6, 8, 10, 12, 14, 18] if _x[2] == 7 else [2, 8, 12, 14, 18, 20, 24, 30]) if _x[1] == "E" else [2, 6, 8, 12] if _x[1] == "F" else [2, 6],
)Examples
Properties #
the exponents of
live ↗InOut
Known value · Bourbaki, Groupes et algèbres de Lie, chapitre VI, planches I-IX
the exponents of
live ↗InOut
Known value · Bourbaki, Groupes et algèbres de Lie, chapitre VI, planches I-IX
the exponents of
live ↗InOut
Known value · Bourbaki, Groupes et algèbres de Lie, chapitre VI, planches I-IX
the exponents of
live ↗InOut
Known value · Bourbaki, Groupes et algèbres de Lie, chapitre VI, planches I-IX
the exponents of
live ↗InOut
Known value · Bourbaki, Groupes et algèbres de Lie, chapitre VI, planches I-IX
About
| Examples | 7 |
|---|