Can I get the invariant subspaces of a matrix group action?

asked 12 years ago

Daniel McLaury gravatar image

updated 12 years ago

Suppose I have a [EDIT: finitely-generated] matrix group GGLn, acting on V=kn in the usual way. Is there some way to calculate the G-invariant subspaces of V? Failing that, is there an easy way to ask if V is irreducible as a G-module?

Preview: (hide)

Comments

The answer depends on G. Is it a finite group? A big group? Do you have a concrete example?

vdelecroix gravatar imagevdelecroix ( 12 years ago )

Let's say not necessarily a finite group, but generated by two or three explicitly-given matrices.

Daniel McLaury gravatar imageDaniel McLaury ( 12 years ago )

First of all you can check if your group is Zariski dense. Nothing is ready made in Sage but you may use different strategy but one is described here http://mathoverflow.net/questions/101874/computing-the-zariski-closure-of-a-subgroup-of-sln-z. You may also try to compute the Lie algebra of the Zariski closure.

vdelecroix gravatar imagevdelecroix ( 11 years ago )