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Producing subgroups of Weyl groups

asked 13 years ago

updated 10 years ago

FrédéricC gravatar image

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

Given some elements SW, 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 8 years ago

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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: 13 years ago

Seen: 809 times

Last updated: Jan 04 '12