SymTensorProductDecomposition( module, HM )
module is a module for a matrix group G over a finite field. HM is
the module corresponding to the action of a subgroup H of G on the
same vector space. Both G and H are assumed to act absolutely
irreducibly. The function returns true if HM can be decomposed as a
tensor product of two or more H-modules, all of the same dimension,
where these tensor factors are permuted by the action of G. In this
case, components of module record the tensor decomposition and the
action of G in permuting the factors. If no such decomposition is
found, SymTensorProductDecomposition returns false.
A negative answer is not reliable, since we try to find a decomposition of HM as a tensor product only by considering some pseudo-random elements.
SymTensorProductDecomposition is called by SmashGModule.
The algorithm is described in [6].
GAP 3.4.4