Question

It is important to remember that the same grouping of orbitals will have different summetry labels whaen you solve for their irreducible res in different point grouos

Answer 1

A reducible representation is one that has a proper invariant subspace; a completely reducible representation is one where every invariant subspace splits (i.e., is a direct summand as representations). Let W⊂V be an irrep over a ground field k !