ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 28 Mar 2013 15:07:06 +0100Can I get the invariant subspaces of a matrix group action?https://ask.sagemath.org/question/8971/can-i-get-the-invariant-subspaces-of-a-matrix-group-action/Suppose I have a [EDIT: finitely-generated] matrix group $G \leq GL_n$, acting on $V = k^n$ 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?Thu, 07 Jun 2012 18:58:55 +0200https://ask.sagemath.org/question/8971/can-i-get-the-invariant-subspaces-of-a-matrix-group-action/Comment by Daniel McLaury for <p>Suppose I have a [EDIT: finitely-generated] matrix group $G \leq GL_n$, acting on $V = k^n$ 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?</p>
https://ask.sagemath.org/question/8971/can-i-get-the-invariant-subspaces-of-a-matrix-group-action/?comment=18478#post-id-18478Let's say not necessarily a finite group, but generated by two or three explicitly-given matrices.Fri, 28 Dec 2012 04:43:08 +0100https://ask.sagemath.org/question/8971/can-i-get-the-invariant-subspaces-of-a-matrix-group-action/?comment=18478#post-id-18478Comment by vdelecroix for <p>Suppose I have a [EDIT: finitely-generated] matrix group $G \leq GL_n$, acting on $V = k^n$ 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?</p>
https://ask.sagemath.org/question/8971/can-i-get-the-invariant-subspaces-of-a-matrix-group-action/?comment=18004#post-id-18004First 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.Thu, 28 Mar 2013 15:07:06 +0100https://ask.sagemath.org/question/8971/can-i-get-the-invariant-subspaces-of-a-matrix-group-action/?comment=18004#post-id-18004Comment by vdelecroix for <p>Suppose I have a [EDIT: finitely-generated] matrix group $G \leq GL_n$, acting on $V = k^n$ 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?</p>
https://ask.sagemath.org/question/8971/can-i-get-the-invariant-subspaces-of-a-matrix-group-action/?comment=19283#post-id-19283The answer depends on G. Is it a finite group? A big group? Do you have a concrete example?Sat, 04 Aug 2012 03:51:00 +0200https://ask.sagemath.org/question/8971/can-i-get-the-invariant-subspaces-of-a-matrix-group-action/?comment=19283#post-id-19283