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Statistic identifier: St000821

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Collection: Finite Cartan types

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Description: The determinant of the Cartan matrix.

This is also the order of the center of the corresponding simply connected group.

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References: [1]   [[wikipedia:Cartan matrix#Determinants of the Cartan matrices of the simple Lie algebras]]

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Code:
def statistic(t):
    return det(CartanMatrix(t))


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Statistic values:

['A',1] => 2
['A',2] => 3
['B',2] => 2
['G',2] => 1
['A',3] => 4
['B',3] => 2
['C',3] => 2
['A',4] => 5
['B',4] => 2
['C',4] => 2
['D',4] => 4
['F',4] => 1
['A',5] => 6
['B',5] => 2
['C',5] => 2
['D',5] => 4
['A',6] => 7
['B',6] => 2
['C',6] => 2
['D',6] => 4
['E',6] => 3
['A',7] => 8
['B',7] => 2
['C',7] => 2
['D',7] => 4
['E',7] => 2
['A',8] => 9
['B',8] => 2
['C',8] => 2
['D',8] => 4
['E',8] => 1

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Created: May 23, 2017 at 15:29 by Martin Rubey

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Last Updated: May 23, 2017 at 15:29 by Martin Rubey