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In this paper, we propose a general implementation of the Virasoro generatorsand Kac-Moody currents in generic tensor network representations of2-dimensional critical lattice models. Our proposal works even when a quantumHamiltonian of the lattice model is not available, which is the case in manynumerical computations involving numerical blockings. We tested our proposal onthe 2d Ising model, and also the dimer model, which works to high accuracy evenwith a fairly small system size. Our method makes use of eigenstates of a smallcylinder to generate descendant states in a larger cylinder, suggesting someintricate algebraic relations between lattice of different sizes.

Virasoro and Kac-Moody algebra in generic tensor network representations of 2d critical lattice partition functions