DynkinIndex

The Dynkin index of the Lie algebra: the greatest common divisor of the indices of its representations.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001156via CartanType✓↗

DynkinIndex(cartanType)The Dynkin index of the Lie algebra: the greatest common divisor of the indices of its representations.

Typed signatures

Type	Package	Applies
(cartan_type) -> number	combinatorics	always

Domain: Cartan type statistics

Details

• Defined over CartanType as an expression in _x, evaluated by compute-engine — the definition IS the implementation.
• Takes a CartanType and 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

1 if _x[1] == "A" else (1 if _x[2] == 2 else 2) if _x[1] == "B" else 1 if _x[1] ==
                                                                          "C" else 2 if _x[1] == "D" else (6 if _x[2] == 6 else 12 if _x[2] == 7 else 60) if _x[1] == "E" else 6 if _x[1] == "F" else 2

Examples

Basic #

the type $D_5$

live ↗

In$\mathrm{DynkinIndex}(\operatorname{CartanType}((\text{D},5)))$Out$2$

the type $E_6$

live ↗

In$\mathrm{DynkinIndex}(\operatorname{CartanType}((\text{E},6)))$Out$6$

Properties #

FindStat's value for ['A',1]

live ↗

In$\mathrm{CombinatorialStat}(\operatorname{CartanType}(("A",1)), \text{DynkinIndex})$Out$1$

Known value · FindStat St001156

FindStat's value for ['A',2]

live ↗

In$\mathrm{CombinatorialStat}(\operatorname{CartanType}(("A",2)), \text{DynkinIndex})$Out$1$

Known value · FindStat St001156

FindStat's value for ['A',3]

live ↗

In$\mathrm{CombinatorialStat}(\operatorname{CartanType}(("A",3)), \text{DynkinIndex})$Out$1$

Known value · FindStat St001156

About

Examples	5
Crosswalk	FindStat