Identifier
Identifier
Values
['A',9] generating graphics... => 1
['B',9] generating graphics... => 2
['C',9] generating graphics... => 1
['D',9] generating graphics... => 2
['A',10] generating graphics... => 1
['B',10] generating graphics... => 2
['C',10] generating graphics... => 1
['D',10] generating graphics... => 2
['A',1] generating graphics... => 1
['A',2] generating graphics... => 1
['B',2] generating graphics... => 1
['G',2] generating graphics... => 2
['A',3] generating graphics... => 1
['B',3] generating graphics... => 2
['C',3] generating graphics... => 1
['A',4] generating graphics... => 1
['B',4] generating graphics... => 2
['C',4] generating graphics... => 1
['D',4] generating graphics... => 2
['F',4] generating graphics... => 6
['A',5] generating graphics... => 1
['B',5] generating graphics... => 2
['C',5] generating graphics... => 1
['D',5] generating graphics... => 2
['A',6] generating graphics... => 1
['B',6] generating graphics... => 2
['C',6] generating graphics... => 1
['D',6] generating graphics... => 2
['E',6] generating graphics... => 6
['A',7] generating graphics... => 1
['B',7] generating graphics... => 2
['C',7] generating graphics... => 1
['D',7] generating graphics... => 2
['E',7] generating graphics... => 12
['A',8] generating graphics... => 1
['B',8] generating graphics... => 2
['C',8] generating graphics... => 1
['D',8] generating graphics... => 2
['E',8] generating graphics... => 60
click to show generating function       
Description
The Dynkin index of the Lie algebra of given type.
This is the greatest common divisor of the Dynkin indices of the representations of the Lie algebra. It is computed in [2, prop.2.6].
References
[1] wikipedia:Dynkin index
[2] Laszlo, Y., Sorger, C. The line bundles on the moduli of parabolic $G$-bundles over curves and their sections MathSciNet:1456243
Code
def statistic(C):
    n = C.rank()
    T = C.type()
    if T in ["A", "C"]:
        return 1
    if T == "B":
        if n == 2:
            return 1
        if n >= 3:
            return 2
    if T == "D":
        if n >= 4:
            return 2
    if T == "E":
        if n == 6:
            return 6
        if n == 7:
            return 12
        if n == 8:
            return 60
    if T == "F":
        return 6
    if T == "G":
        return 2
Created
Apr 20, 2018 at 21:31 by Martin Rubey
Updated
Apr 20, 2018 at 21:31 by Martin Rubey