The ability of positronium to form both singlet and triplet states is described mathematically by saying that the product of two doublet representations (meaning the electron and positron, which are both spin  doublets) can be decomposed into the sum of an adjoint representation (the triplet or spin 1 state) and a trivial representation (the singlet or spin 0 state). While the particle interpretation of the positronium triplet and singlet states is arguably more intuitive, the mathematical description enables precise calculations of quantum states and probabilities.