 The vacuum representation "H"0 of an affine Kac–Moody algebra at a fixed level can be encoded in a vertex algebra.The derivation acts as the energy operator "L"0 on "H"0, which can be written as a direct sum of the non-negative integer eigenspaces of "L"0, the zero energy space being generated by the vacuum vector Ω.The eigenvalue of an eigenvector of "L"0 is called its energy.