EXTENSIONS OF THE JACOBI IDENTITY FOR RELATIVE UNTWISTED VERTEX OPERATORS, AND GENERATING FUNCTION IDENTITIES FOR UNTWISTED STANDARD MODULES - THE A(1)(1)-CASE

In this paper, which extends the author's previous work [6] on relative Z2-twisted vertex operators and twisted standard A1(1)-modules, the Jacobi identity for relative untwisted vertex operators, discovered by Dong and Lepowsky, is extended to multi-operator identities in the case of the A1(1)-lattice. Particular coefficients of these identifies (coefficients of monomials in some of the formal variables of the identities) give generating function identities for untwisted standard A1(1)-modules. This procedure (together with Husu [6], Sections 2 and 3) discloses the analogy (from the point of view of relative vertex operators) between the constructions of twisted and untwisted standard A1(1)-representations. Moreover, exhibiting relative multi-operator identities and extracting coefficients of these identities at once, this procedure shows a method to improve and simplify the Z2-twisted counterpart procedure of constructing generating function identities for Z2-twisted standard A1(1)-modules in Husu (to appear), Section 3.