Theory of Generalized coherent states of the groups $SU_n$

Close connection between algebraic properties of generalised coherent states (GCS) and algebras of generating invariants of $SU_n$ groups is established. Methods of calculating the matrix elements in GCS of finite transformations and generators of $SU_n$ groups and also finding the coefficients (analogous to the Klebsch–Gordan coefficients) of expansions of GCS products over the GCS of $SU_n$ groups are presented. Possibilities of applications of the results obtained to the theory of the interaction between the radiation and substance are discussed.