cplx_isotypic_decomposition

cplx_isotypic_decomposition(G, rep)

Perform the isotypic decomposition of a unitary representation.

This routine decomposes the representation into complex irreducibles.

Parameters:

• G (Group) – Symmetry group of the representation.

• rep (dict | collections.abc.Callable) – A Union-style input. It must be either a dict or a collections.abc.Callable. It must map each GroupElement to a matrix ndarray.

Returns:

List of complex irreducible representations, sorted in ascending order of

dimension.

Q (ndarray): Hermitian matrix such that Q @ rep[g] @ Q^-1 is block diagonal, with blocks

sorted_irreps.

Return type:

sorted_irreps (list[dict])