Extensions of the Jacobi identity for relative untwisted vertex operators, and generating function identities for untwisted standard modules: The \(A^{(1)}_ 1\)-case
The Jacobi identity for two relative untwisted vertex operators was given by \textit{C. Dong} and \textit{J. Lepowsky} [Proc. XIIth Int. Colloq. on Group Theoretical Methods in Physics, Ste-Adele 1988, 235-238 (World Scientific, Singapore, 1989)]. The author of this paper extends the Jacobi identity to an analogue for a finite number of relative untwisted vertex operators associated with the \(A_1\)-root lattice. Such an extension can be used to reinterpret certain results in \textit{J. Lepowsky} and \textit{R. L. Wilson}'s work on the standard modules of \(A_1^{(1)}\) [Invent. Math. 79, 417-442 (1985; Zbl 0577.17010)], and \textit{J. Lepowsky} and \textit{M. Primc}'s work [Contemp. Math. 46 (1985; Zbl 0569.17007)].
scientific article; zbMATH DE number 741484
scientific article