Small clusters: Dynamical symmetry and $1/d$ expansion

Asymptotic expansion on the parameter $1/d$, where $d$ is space dimension, is built for the spectrum of critical binding constants of three and four particle clusters. Trajectories of bound states in the “energy – binding constant” plane are investigated. Asymptotical dynamical symmetry of the problem is found and applied to the reduction of the problem to dynamics on (semi) simple Lie algebra.