- FindStat

Identifier

St000861: Finite Cartan types ⟶ ℤ

Values

=>
                            Cc0022;cc-rep
                            
                            
                            

                        ['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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Description

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

Code

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

Created

Jun 25, 2017 at 20:00 by Christian Stump

Updated

Jun 25, 2017 at 20:00 by Christian Stump