- FindStat

Identifier

St001749: 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]=>4
['B',4]=>6
['C',4]=>6
['D',4]=>6
['F',4]=>8
['A',5]=>5
['B',5]=>7
['C',5]=>7
['D',5]=>7
['A',6]=>7
['B',6]=>14
['C',6]=>14
['D',6]=>13
['E',6]=>12
['A',7]=>12
['B',7]=>16
['C',7]=>16
['D',7]=>16
['E',7]=>22
['A',8]=>15
['B',8]=>29
['C',8]=>29
['D',8]=>30
['E',8]=>52
                    

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Description

The number of distinct dimensions of the irreducible representations of the Weyl group of a finite Cartan type.

Code

def statistic(ct):
    G = WeylGroup(ct, implementation="permutation").gap()
    id = G.Identity()
    return len(set((id^r).sage() for r in G.Irr()))

Created

Nov 29, 2021 at 10:30 by Martin Rubey

Updated

Nov 29, 2021 at 10:30 by Martin Rubey