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Identifier
Values
['A',1] => 2
['A',2] => 3
['B',2] => 5
['G',2] => 7
['A',3] => 4
['B',3] => 7
['C',3] => 6
['A',4] => 5
['B',4] => 9
['C',4] => 8
['D',4] => 8
['F',4] => 52
['A',5] => 6
['B',5] => 11
['C',5] => 10
['D',5] => 10
['A',6] => 7
['B',6] => 13
['C',6] => 12
['D',6] => 12
['E',6] => 27
['A',7] => 8
['B',7] => 15
['C',7] => 14
['D',7] => 14
['E',7] => 133
['A',8] => 9
['B',8] => 17
['C',8] => 16
['D',8] => 16
['C',2] => 4
['A',9] => 10
['B',9] => 19
['C',9] => 18
['D',9] => 18
['A',10] => 11
['B',10] => 21
['C',10] => 20
['D',10] => 20
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Description
The dimension of the representation $V(\Lambda_1)$.
The sizes of $E_6$ and $E_7$ can be seen in [1].
References
[1] Jones, B., Schilling, A. Affine structures and a tableau model for $E_6$ crystals MathSciNet:2684152
Code
def statistic(ct):
    if ct.letter in ['A','B','C','D']:
        return crystals.Letters(ct).cardinality()
    elif ct.letter == 'E':
        if ct.rank() == 6:
            B = KirillovReshetikhinCrystal(['E',6,1], 1,1)
            return B.cardinality()
        elif ct.rank() == 7:
            La = C.root_system().weight_lattice().fundamental_weight(1)     
            T = HighestWeightCrystal(La)
            return T.cardinality()
        elif ct.rank() == 8:
            RC = RiggedConfigurations(['E',8,1], [[1,1]])
            return CT.cardinality()
    elif ct.letter == 'F' and ct.rank() == 4:
        RC = RiggedConfigurations(['F',4,1], [[1,1]])
        return RC.cardinality()
Created
Jun 14, 2013 at 16:37 by Travis Scrimshaw
Updated
Dec 29, 2016 at 09:20 by Christian Stump