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Identifier
Values
=>
Cc0022;cc-rep
['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