Conformal field theory
The Hilbert space of physical states is a unitary module of the Virasoro algebra corresponding to a fixed value of "c". Stability requires that the energy spectrum of the Hamiltonian be nonnegative. The modules of interest are the highest weight modules of the Virasoro algebra.
Hilbert cube
Every G-subset of the Hilbert cube is a Polish space, a topological space homeomorphic to a separable and complete metric space. Conversely, every Polish space is homeomorphic to a G-subset of the Hilbert cube.