Feigin, B. L.; Fuks, D. B. Representations of the Virasoro algebra. (English) Zbl 0722.17020 Representation of Lie groups and related topics, Adv. Stud. Contemp. Math. 7, 465-554 (1990). [For the entire collection see Zbl 0714.00007.] This most comprehensive treatise on the representation theory of the famous Virasoro algebra was preprinted 10 years ago, but apart from a version (marred by funny English) preprinted in D. Leites (ed.), Seminar on supermanifolds No.4, Reports of Stockholm University (1987), this important work was unavailable. The paper contains a detailed description of Verma modules and the modules of semi-infinite forms (in particular, the space of semi-infinite forms is endowed with \(\mathfrak{gl}(\infty)\)-, \(\mathfrak{sp}(2\infty)\) or an \(\mathfrak o(\infty)\)-module structure). The intertwining operators between modules of semi-infinite forms over the Virasoro algebra are identified as “vertex operators” of physicists. The vertex operators are studied in detail: they are instrumental in the proofs of the main theorems and elsewhere. Proofs are lucid. Reviewer: D. Leites (Stockholm) Cited in 4 ReviewsCited in 36 Documents MSC: 17B68 Virasoro and related algebras 17B69 Vertex operators; vertex operator algebras and related structures 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) Keywords:representation; Virasoro algebra; Verma modules; modules of semi-infinite forms; intertwining operators; vertex operators Citations:Zbl 0714.00007 PDFBibTeX XML