 Every other integral representation "Hi" at the same level becomes a module for the vertex algebra, in the sense that for each "a" there is a vertex operator on "Hi" such that

The most general vertex operators at a given level are intertwining operators between representations "Hi" and "H""j" where "v" lies in "H""k".These operators can also be written as

but δ can now be rational numbers.Again these intertwining operators are characterized by properties

and relations with "L"0 and "L"−1 similar to those above.