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 series and Hilbert polynomial
The Hilbert function
maps the integer onto the dimension of the -vector space . The Hilbert series, which is called Hilbert–Poincaré series in the more general setting of graded vector spaces, is the formal series