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Unitary representations of some infinite dimensional groups. (English) Zbl 0495.22017

22E70 Applications of Lie groups to the sciences; explicit representations
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
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[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)
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