Neretin, Yu. A. Spinor representation of the infinite-dimensional orthogonal semigroup and the Virasoro algebra. (Russian) Zbl 0693.17010 Funkts. Anal. Prilozh. 23, No. 3, 32-44 (1989). The author considers a category of pairs of Hilbert spaces \((V_+,V_- )\) with a fixed antilinear isometry mapping \(V_-\) onto \(V_+\) and morphisms defined by block matrices with Hilbert-Schmidt operators in the diagonal. A projective representation Spin by operators on a Fermion Fock space \(\Lambda (V_+)\) endowed with a family of seminorms making it a FrĂ©chet space generated by the Grassmann products of basis elements of \(V_+\) is defined and studied on various subcategories. It is proved, that an irreducible highest weight representation of the Virasoro algebra is integrable to a projective representation of the group \(\mathrm{Diff}\) of analytic orientation preserving diffeomorphisms of the circle. This representation extends to a projective representation of a semigroup, which was defined by the author as the complexification of \(\mathrm{Diff}\) [compare the author’s paper in ibid. 21, No. 2, 82–83 (1987; Zbl 0628.58004)]. Moreover it is stated, that every irreducible highest weight representation of the Virasoro algebra admits a realization by sections in a holomorphic linear bundle on a Siegel-Kirillov domain. Reviewer: Helmut Boseck (Greifswald) Cited in 1 ReviewCited in 2 Documents MSC: 17B68 Virasoro and related algebras 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) 22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds Keywords:diffeomorphism group of the circle; Fermion Fock space; irreducible highest weight representation; Virasoro algebra; projective representation; analytic orientation preserving diffeomorphisms; linear bundle; Siegel-Kirillov domain Citations:Zbl 0628.58004 PDFBibTeX XMLCite \textit{Yu. A. Neretin}, Funkts. Anal. Prilozh. 23, No. 3, 32--44 (1989; Zbl 0693.17010)