 When "v" is in the lowest energy subspace for "L"0 on "Hk", an irreducible representation of formula_5, the operator is called a primary field of charge "k".Given a chain of "n" primary fields starting and ending at "H"0, their correlation or "n"-point function is defined by

In the physics literature the "v""i" are often suppressed and the primary field written Φ"i"("zi"), with the understanding that it is labelled by the corresponding irreducible representation of formula_5.If ("X""s") is an orthonormal basis of formula_5 for the Killing form, the Knizhnik–Zamolodchikov equations may be deduced by integrating the correlation function

first in the "w" variable around a small circle centred at "z"; by Cauchy's theorem the result can be expressed as sum of integrals around "n" small circles centred at the "z""j"'s