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Statistic identifier: St000861

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Collection: Finite Cartan types

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Description: The maximal dimension of an irreducible representation of the Weyl group of a finite Cartan type.

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References: 

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Code:
def statistic(cartan_type):
    W = ReflectionGroup(cartan_type)
    return max( chi(W.one()) for chi in W.irreducible_characters() )


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Statistic values:

['A',1] => 1
['A',2] => 2
['B',2] => 2
['G',2] => 2
['A',3] => 3
['B',3] => 3
['C',3] => 3
['A',4] => 6
['B',4] => 8
['C',4] => 8
['D',4] => 8
['F',4] => 16
['A',5] => 16
['B',5] => 20
['C',5] => 20
['D',5] => 20
['A',6] => 35
['B',6] => 80
['C',6] => 80
['D',6] => 45
['E',6] => 90
['A',7] => 90
['B',7] => 210
['C',7] => 210
['D',7] => 210
['E',7] => 512
['A',8] => 216
['B',8] => 672
['C',8] => 672
['D',8] => 672
['E',8] => 7168

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Created: Jun 25, 2017 at 20:00 by Christian Stump

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Last Updated: Jun 25, 2017 at 20:00 by Christian Stump