Identifier
Identifier
Values
['A',9] => 1
['B',9] => 2
['C',9] => 1
['D',9] => 2
['A',10] => 1
['B',10] => 2
['C',10] => 1
['D',10] => 2
['A',1] => 1
['A',2] => 1
['B',2] => 1
['G',2] => 2
['A',3] => 1
['B',3] => 2
['C',3] => 1
['A',4] => 1
['B',4] => 2
['C',4] => 1
['D',4] => 2
['F',4] => 6
['A',5] => 1
['B',5] => 2
['C',5] => 1
['D',5] => 2
['A',6] => 1
['B',6] => 2
['C',6] => 1
['D',6] => 2
['E',6] => 6
['A',7] => 1
['B',7] => 2
['C',7] => 1
['D',7] => 2
['E',7] => 12
['A',8] => 1
['B',8] => 2
['C',8] => 1
['D',8] => 2
['E',8] => 60
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
 wikipedia:Dynkin index
 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