[BUG] splitdims(::BlockSparseArrays, ::Tuple{AbstractGradedUnitRanges) result is wrong

[ogauthe]

Still investigating ITensor/TensorAlgebra.jl#29

There is something wrong with splitdims, with a mix-up between tensor_product and fusion_product. The issue is around

BlockSparseArrays.jl/ext/BlockSparseArraysTensorAlgebraExt/BlockSparseArraysTensorAlgebraExt.jl:88

function TensorAlgebra.splitdims(
  ::SectorFusion, a::AbstractArray, split_axes::AbstractUnitRange...
)

I currently believe TensorAlgebra is fine and the test in ITensor/TensorAlgebra.jl#29 should pass on the issue here has been fixed.

[ogauthe]

I believe a_unblocked = a[axes_prod...] is wrong. a has fused axes, as produced with TensorAlgebra.fusedims, equivalent to what GradedUnitRanges.fusion_product would output. It cannot be indexed with axes_prod which are tensor product axes, i.e. without blockmergesort. Coefficient permutation is lost in the process.