  We consider an ensemble of atoms with $\Lambda$-type level structure trapped
in a single-mode cavity, and propose a geometric scheme of coherent
manipulation of quantum states on the subspace of zero-energy states within the
quantum Zeno subspace of the system. We find that the particular subspace
inherits the decoherence-free nature of the quantum Zeno subspace and features
a symmetry-protected degeneracy, fulfilling all the conditions for a universal
scheme of arbitrary unitary operations on it.
