Create an alternative: W(E8) act on positive roots to get some roots

asked 2014-08-17 19:13:57 +0200

Biswajit gravatar image

updated 2015-01-14 11:36:29 +0200

FrédéricC gravatar image


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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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 ( 2014-08-19 22:45:07 +0200 )edit

yes it works for A4 or A6 or A8 . E8 is too big

Biswajit gravatar imageBiswajit ( 2014-08-20 09:07:38 +0200 )edit

Up to multiplication by the simple reflection $s_1$, these elements live in the stabilizer of $\alpha_1$. you should rather iterate over this stabilizer.

FrédéricC gravatar imageFrédéricC ( 2014-08-20 22:59:33 +0200 )edit