Request to add feature: Decomposing a finite dimensional vector space with respect to a collection of matrices acting on the vector space.

[sagetrac-chrisjamesberg]

I would like to request a new feature for Sage. I would like to be able to input a collection of n by n matrices which I think of as acting on an n dimensional vector space and have sage output a decomposition of the vector space into irreducible components with respect to the action of these matrices.

addendum: it would even be better to have a method that provides the finest decomposition up to subgroups of finite index!

Component: algebra

Keywords: days30, days88

Issue created by migration from https://trac.sagemath.org/ticket/11285

[saliola]

Changed keywords from none to days30

[tscrim]

comment:3

I've uploaded the start of a patch which works well if the basis is suitably chosen. I just apply all the matrices and see where it takes the natural basis vectors, and merges into appropriate subspaces. In the documentation there is the start of a good test example if anyone can get this to work...

[tscrim]

Attachment: trac_11285-decompose_vecspace-ts.patch.gz

[nthiery]

comment:4

Hi Travis,

You want to get in touch with Aladin, for this is decomposing a module for a general finite dimensional algebra, and he is working on the representation theory of those algebras.

[saliola]

Changed keywords from days30 to days30, days88