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Identifier
Values
=>
Cc0022;cc-rep
['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