- FindStat

Identifier

St001154: Finite Cartan types ⟶ ℤ

Values

=>
                            Cc0022;cc-rep
                            
                            
                            

                        ['A',1]=>2
['A',2]=>3
['B',2]=>3
['G',2]=>4
['A',3]=>4
['B',3]=>5
['C',3]=>4
['A',4]=>5
['B',4]=>7
['C',4]=>5
['D',4]=>6
['F',4]=>9
['A',5]=>6
['B',5]=>9
['C',5]=>6
['D',5]=>8
['A',6]=>7
['B',6]=>11
['C',6]=>7
['D',6]=>10
['E',6]=>12
['A',7]=>8
['B',7]=>13
['C',7]=>8
['D',7]=>12
['E',7]=>18
['A',8]=>9
['B',8]=>15
['C',8]=>9
['D',8]=>14
['E',8]=>30
                    

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Description

The dual Coxeter number of a finite Cartan type.

References

[1] Humphreys, J. What role does the "dual Coxeter number" play in Lie theory (and should it be called the "Kac number")? MathOverflow:25592

Code

def statistic(C):
    return C.dual_coxeter_number()

Created

Apr 20, 2018 at 20:27 by Martin Rubey

Updated

Apr 20, 2018 at 20:27 by Martin Rubey