  A model is proposed for the spectrum of $\Lambda$ hypernuclei based on the
$u(3)\times u(2)$ Lie algebra, in which the internal degrees of freedom of the
spin-1/2 $\Lambda$ particle are treated in the Fermionic $u(2)$ scheme, while
the motion of the hyperon inside a nucleus is described in the Bosonic $u(3)$
harmonic oscillator scheme. Within this model, a simple formula for
single-particle energies of the $\Lambda$ particle is obtained from the natural
dynamical symmetry. The formula is applied to the experimental data on the
reaction spectroscopy for the $^{89}_\Lambda$Y and $^{51}_\Lambda$V
hypernuclei, providing a clear theoretical interpretation of the observed
structures.
