- FindStat

Identifier

St001897: Finite Cartan types ⟶ ℤ

Values

=>
                            Cc0022;cc-rep
                            
                            
                            

                        ['A',1]=>2
['A',2]=>3
['B',2]=>4
['G',2]=>6
['A',3]=>4
['B',3]=>6
['C',3]=>6
['A',4]=>5
['B',4]=>8
['C',4]=>8
['D',4]=>8
['F',4]=>24
['A',5]=>6
['B',5]=>10
['C',5]=>10
['D',5]=>10
['A',6]=>7
['B',6]=>12
['C',6]=>12
['D',6]=>12
['E',6]=>27
['A',7]=>8
['B',7]=>14
['C',7]=>14
['D',7]=>14
['E',7]=>56
['A',8]=>9
['B',8]=>16
['C',8]=>16
['D',8]=>16
['E',8]=>240
                    

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Description

The minimal degree of a faithful permutation representation of a Weyl group.
Data are from [1, Table 1].

References

[1] Stembridge, J. R. Computational aspects of root systems, Coxeter groups, and Weyl characters MathSciNet:1862148

Code

def statistic(ct):
    if ct.type() == "A":
        return ct.rank() + 1
    if ct.type() in ["B", "C", "D"]:
        return 2*ct.rank()
    if ct.type() == "G" and ct.rank() == 2:
        return 6
    if ct.type() == "F" and ct.rank() == 4:
        return 24
    if ct.type() == "E" and ct.rank() == 6:
        return 27
    if ct.type() == "E" and ct.rank() == 7:
        return 56
    if ct.type() == "E" and ct.rank() == 8:
        return 240

Created

Apr 12, 2023 at 16:12 by Martin Rubey

Updated

Apr 12, 2023 at 16:12 by Martin Rubey