Does anyone have a program written in Mathematica (or SAGE or GAP) that computes the invariant subspace lattice of a matrix group?
2026-03-28 04:00:52.1774670452
Computing Invariant Subspaces of Matrix Groups
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I am posting a CW answer to remove this question from the unanswered queue. Thanks to @Derek Holt and @Jack Schmidt for the comments that I've converted to the answer
It depends a little on the matrix group. If the matrix group is the one element group over the 6x6 matrices over Z/11Z then the lattice has 3 billion subspaces. If the associated module is "square-free" then things are much nicer, and GAP can handle this without trouble. The GAP command for this is
MTX.BasesSubmoduleswhich is described in the Meataxe chapter.MTX.BasesMinimalSubmodulesandMTX.BasesMaximalSubmodulesare also useful if there are too many of them.