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Identifier
Values
['A',1] => 2
['A',2] => 3
['B',2] => 4
['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] => 26
['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] => 56
['A',8] => 9
['B',8] => 17
['C',8] => 16
['D',8] => 16
['E',8] => 248
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Description
The minimal dimension of a faithful linear representation of the Lie algebra of given type.
References
[1] Burde, D., Moens, W. Minimal faithful representations of reductive Lie algebras MathSciNet:2371687
Code
def statistic(C):
    n = C.rank()
    T = C.type()
    if T == "A":
        return n+1
    if T == "B":
        if n == 2:
            return 4
        if n >= 3:
            return 2*n+1
    if T == "C":
        if n >= 3:
            return 2*n
    if T == "D":
        if n >= 4:
            return 2*n
    if T == "E":
        if n == 6:
            return 27
        if n == 7:
            return 56
        if n == 8:
            return 248
    if T == "F":
        return 26
    if T == "G":
        return 7
Created
Apr 19, 2018 at 19:57 by Martin Rubey
Updated
Apr 19, 2018 at 19:57 by Martin Rubey