**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].

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]

[2]

**Laszlo, Y., Sorger, C.***The line bundles on the moduli of parabolic $G$-bundles over curves and their sections*MathSciNet:1456243Code

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**searching the database

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