Unitary dynamical symmetry in a system of superradiant molecules and the classical limit

Commutative functions corresponding to operators in subspaces of irreducible representations of unitary groups are used to calculate the correlation functions responsible for the statistical properties of coherent spontaneous radiation (superradiation) in a system of many-level molecules. When the quantum mean values over the states of the emitters are calculated in this way, there is no need to label the basis functions of the subspaces of irreducible representations. A method is found for expanding'the mean values near the classical limit $N\to\infty$ in powers of $N^{-1}$, where $N$ is the number of emitters. The properties of coherent states of unitary groups acting in the subspaces of irreducible representations are discussed.