Algorithms for SU(n) boson realizations and D-functions

Boson realizations map operators and states of groups to transformations and states of bosonic systems. We devise a graph-theoretic algorithm to construct the boson realizations of the canonical SU$(n)$ basis states, which reduce the canonical subgroup chain, for arbitrary $n$. The boson realizations are employed to construct $\mathcal{D}$-functions, which are the matrix elements of arbitrary irreducible representations, of SU$(n)$ in the canonical basis. We demonstrate that our $\mathcal{D}$-function algorithm offers significant advantage over the two competing procedures, namely factorization and exponentiation.