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

[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!

[tscrim]

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...

[nthiery]

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.