Extensions of the Jacobi identity for relative untwisted vertex operators, and generating function identities for untwisted standard modules: The A(1)1-case Original Research Article

In this paper, which extends the authorʹs previous work [6] on relative Z2-twisted vertex operators and twisted standard A(1)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 A(1)1-lattice. Particular coefficients of these identities (coefficients of monomials in some of the formal variables of the identities) give generating function identities for untwisted standard A(1)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 A(1)1-representations. Moreover, exhibiting relative multioperator 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 A(1)1-modules in Husu (to appear), Section 3.