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Producing subgroups of Weyl groups

asked 2012-01-04 08:42:04 -0500

updated 2015-01-14 04:36:46 -0500

FrédéricC gravatar image

Let W be a Weyl group, e.g. W = RootSystem('[A, 4]').weight_lattice().weyl_group

Given some elements $S \subset W$, I would like to produce the subgroup generated by $S$. It seems like there are methods in SAGE to do this when W is an abstract group, but I can't see how to do it when $W$ is a Weyl group. Any suggestions?

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answered 2017-02-25 17:08:32 -0500

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There is no general answer to be good enough for special choices of $S$. Using the general group methods the following is working:

# W = RootSystem('[A, 4]').weight_lattice().weyl_group    # does not work 

W = RootSystem( [ 'A', 4 ] ).weight_lattice().weyl_group()
some_elements = [ W.random_element() for _ in range( 3 ) ]
G = W.subgroup( some_elements )
G . order()
# G.list()[:10]

We simply want, ask for and get the W.subgroup generated by the specified elements.

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Asked: 2012-01-04 08:42:04 -0500

Seen: 88 times

Last updated: Jan 04 '12