  In this paper, we propose a general implementation of the Virasoro generators
and Kac-Moody currents in generic tensor network representations of
2-dimensional critical lattice models. Our proposal works even when a quantum
Hamiltonian of the lattice model is not available, which is the case in many
numerical computations involving numerical blockings. We tested our proposal on
the 2d Ising model, and also the dimer model, which works to high accuracy even
with a fairly small system size. Our method makes use of eigenstates of a small
cylinder to generate descendant states in a larger cylinder, suggesting some
intricate algebraic relations between lattice of different sizes.
