For the two-mode exciton system formed by the quasi-spin-wave collective excitation of many Lambda atoms fixed at the lattice sites of a crystal, we discover a dynamical symmetry depicted by the semidirect product algebra SU2( multiply sign in circle) h(2) in the large N limit with low excitations. With the help of the spectral generating algebra method, we obtain a larger class of exact zero-eigenvalue states adiabatically interpolating between the initial state of photon-type and the final state of quasi-spin-wave exciton-type. The conditions for the adiabatic passage of dark states are shown to be valid, even with the presence of the level degeneracy. These theoretical results can lead to the proposal of a new protocol for implementing quantum memory robust against quantum decoherence.