Segal, Graeme Unitary representations of some infinite dimensional groups. (English) Zbl 0495.22017 Commun. Math. Phys. 80, 301-342 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 7 ReviewsCited in 294 Documents MSC: 22E70 Applications of Lie groups to the sciences; explicit representations 22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties Keywords:diffeomorphism group; projective unitary representations; metaplectic representation; orbit picture; theory of strings × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Frenkel, I. B., Ka?, V. G.: Basic representations of affine Lie algebras and dual resonance models. Inventiones math.62, 23-66 (1980) · Zbl 0493.17010 · doi:10.1007/BF01391662 [2] Gel’fand, I. M., Vilenkin, N. Ya.: Generalized Functions, Vol. 4. New York: Academic Press 1964 [3] Gel’fand, I. M., Fuks, D. B.: Funkt. Anal. Jego Prilozh.2, 92-93 (1968) [4] Goddard, P., Horsley, R.: Nucl. Phys.B111, 272-296 (1976) · doi:10.1016/0550-3213(76)90543-5 [5] Goddard, P., Thorn, C. B.: Phys. Lett.40B, 235-238 (1972) [6] Jacob, M. (ed.): Dual theory. Amsterdam: North-Holland 1974 · Zbl 0315.93013 [7] Ka?, V. G.: Adv. Math.30, 85-136 (1978) · Zbl 0391.17010 · doi:10.1016/0001-8708(78)90033-6 [8] Ka?, V. G.: Contravariant form for infinite- dimensional Lie algebras and superalgebras. (to apper) [9] Ka?, V. G.: Adv. Math.35, 264-273 (1980) · Zbl 0431.17009 · doi:10.1016/0001-8708(80)90052-3 [10] Kirillov, A. A.: Unitary representations of the group of diffeomorphisms of a manifold. (to appear) · Zbl 0515.58009 [11] Lazutkin, V. F., Pankratova, T. F.: Funkt. Anal. Jego Prilozh.9, 41-48 (1975) (Russian) · Zbl 0316.30019 · doi:10.1007/BF01078174 [12] Shale, D.: Trans. Am. Math. Soc.103 149-167 (1962) · doi:10.1090/S0002-9947-1962-0137504-6 [13] Shale, D.: Stinespring, W. F.: J. Math. Mech.14, 315-322 (1965) [14] Vergne, M.: Seconde quantification et groupe symplectique. C. R. Acad. Sci. (Paris),285, A 191-194 (1977) · Zbl 0386.22014 [15] Vershik, A. M., Gel’fand, I. M., Graev, M. I.: Usp. Mat. Nauk30, 1-50 (1975) [16] Vershik, A. M., Gel’fand, I. M., Graev, M. I. Dokl. Akad. Nauk. SSSR232, 745-748 (1977) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.