Representations of the Virasoro algebra from lattice models

W e investigate in details how the Virasoro algebra appears in the scaling lim it of the sim plest lattice m odels ofXXZ orRSOS type. Our approach is straightforward but to our knowledge had never been tried so far. W e sim ply form ulate a conjecture for the lattice stress-energy tensor m otivated by the exact derivation oflattice globalW ard identities. W e then check that the proper algebraic relations are obeyed in the scaling lim it. The latter is under reasonable controlthanks to the Bethe-ansatz solution. The results,which are m ostly num ericalfor technicalreasons,are rem arkably precise. They are also corroborated by exact pieces ofinform ation from various sources,in particular Tem perley-Lieb algebra representation theory.M ostfeaturesoftheVirasoro algebra (like centralterm ,nullvectors,m etric properties...) can thus be observed using the lattice m odels.Thisseem sofgeneralinterestforlattice eld theory,and alsom orespeci cally for nding relationsbetween conform alinvarianceand latticeintegrability,sincebasisforthe irreduciblerepresentationsoftheVirasoro algebra should now follow (atleastin principle) from Bethe-ansatzcom putations.