Create an alternative: W(E8) act on positive roots to get some roots
 
  
 
  
 
 
 
 
 
 
    
        
        asked 10 years ago  
 
 Biswajit gravatar image  
 
 
 
 
    
        
        updated 10 years ago  
 
 FrédéricC gravatar image  
 
 
 
 
 
W=WeylGroup(['E',8])
 
R = RootSystem(['E',8]).root_lattice()
 
alpha = R.simple_roots();alpha
 
[w for w in W if w.action(alpha[1])==(alpha[1]+alpha[2])]
 
Output shows :  gap: cannot extend the workspace any more!
 
*Is their any alternative calculation to simplify the above *
 
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Comments
Does this work with A4 or A6 or A8 instead of E8 ? it could be that E8 is too big, for some reason.
FrédéricC gravatar imageFrédéricC (
    
        10 years ago
    )
yes it works for A4 or A6 or A8 .  E8 is too big
Biswajit gravatar imageBiswajit (
    
        10 years ago
    )
Up to multiplication by the simple reflection s1, these elements live in the stabilizer of α1. you should rather iterate over this stabilizer.
FrédéricC gravatar imageFrédéricC (
    
        10 years ago
    )
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