×
Albeverio, Sergio; Høegh-Krohn, Raphael; Testard, Daniel; Vershik, A.

Factorial representations of path groups. (English) Zbl 0522.22013

J. Funct. Anal. 51, 115-131 (1983).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0522.22013

Cited in 3 Reviews
Cited in 21 Documents

MSC:

22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
22D25 \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations
22E70 Applications of Lie groups to the sciences; explicit representations

Keywords:

factorial representations; path groups; energy representation; compact semisimple Lie group

Citations:

Zbl 0488.22038
PDFBibTeX XMLCite
\textit{S. Albeverio} et al., J. Funct. Anal. 51, 115--131 (1983; Zbl 0522.22013)
Full Text: DOI

References:

[1] Vershik, A.; Gelfand, I.; Graev, M., Russian Math. Surveys, 28, 83-132 (1973), transl. · Zbl 0297.22003
[2] Ismagilov, R., Math. USSR-Sb., 29, 105-117 (1976), transl. · Zbl 0383.22002
[3] Parthasarathy, K.; Schmidt, K., A new method for constructing factorisable representations for current groups and current algebras, Comm. Math. Phys., 50, 167-175 (1976) · Zbl 0332.43009
[4] Vershik, A.; Gelfand, I.; Graev, M., Representations of the group of functions taking values in a compact Lie group, Compositio Math., 42, 217-243 (1981) · Zbl 0449.22019
[5] Albeverio, S.; Høegh-Krohn, R., The energy representation of Sobolev-Lie groups, Compositio Math., 36, 37-52 (1978) · Zbl 0393.22013
[6] Vershik, A.; Gelfand, I.; Graev, M., Representations of the group of smooth mappings of a manifold into a compact Lie group, Compositio Math., 35, 299-334 (1977) · Zbl 0368.53034
[7] Albeverio, S.; Høegh-Krohn, R.; Testard, D., Irreducibility and reducibility for the energy representation of the group of mappings of a Riemannian manifold into a compact semisimple Lie group, J. Funct. Anal., 41, 378-396 (1981) · Zbl 0488.22038
[8] Albeverio, S.; Gallavotti, G.; Høegh-Krohn, R., Some results for the exponential interaction in two or more dimensions, Comm. Math. Phys., 70, 187-192 (1979) · Zbl 0433.60098
[9] Marion, I., Etude du groupe \(G^X\), representations unitaires non localisées d’ordre > 0 (1978), Luminy, Preprint
[10] Frenkel, I. B., Orbital Theory for Affine Lie Algebras (1980), Yale Univ. Press: Yale Univ. Press New Haven, Conn, Preprint · Zbl 0451.17004
[11] Frenkel, I. B.; Kac, V. G., Basic representations of affine Lie algebras and dual resonance models, Invent. Math., 62, 23-66 (1980) · Zbl 0493.17010
[12] Gaveau, B.; Trauber, Ph, Mesures et representations non locales pour les groupes de Lie d’applications, C. R. Acad. Sci. Paris Ser. A, 291, 575-578 (1980) · Zbl 0451.60012
[13] Streater, R. F., Current commutation relations, continuous tensor products and infinitely divisible group representations, (Jost, R., Local Quantum Theory (1969), Academic Press: Academic Press New York), 247-263
[14] Araki, H., Factorisable representations of current algebra, Publ. Res. Inst. Math. Sci., A5, 3, 361-422 (1970) · Zbl 0238.22014
[15] Parthasarathy, K. R.; Schmidt, K., Positive Definite Kernels, Continuous Tensor Products and Central Limit Theorems of Probability Theory, (Lecture Notes in Mathematics, No. 272 (1972), Springer: Springer Berlin) · Zbl 0237.43005
[16] Guichardet, A., Représentations de \(G^X\) selon Gelfand et Delorme, (“Sém. Bourbaki” 28 January 1975-1976, No. 486 (1976)) · Zbl 0344.22008
[17] Vershik, A. M.; Gelfand, I. M.; Graev, M. I., Functional Anal. Appl., 151-153 (1974), transl. · Zbl 0299.22004
[18] Størmer, E., Types of von Neumann algebras associated with extremal invariant states, Comm. Math. Phys., 6, 194-204 (1967) · Zbl 0171.46903
[19] Kac, V. G., Infinite-dimensional Lie algebras and Dedekind’s η-function, Functional Anal. Appl., 8, 68-70 (1974) · Zbl 0299.17005
[20] Garland, H., Dedekind’s η-function and the cohomology of infinite dimensional Lie algebras, (Proc. Nat. Acad. Sci. U.S.A., 72 (1975)), 2493-2495 · Zbl 0322.18010
[21] Macdonald, I. G., Affine root system and Dedekind’s η-function, Invent. Math., 15, 91-143 (1972) · Zbl 0244.17005
[23] Kac, V. G.; Kazhdan, D. A.; Lepowsky, J.; Wilson, R. L., Realization of the Basic Representations of the Euclidean Lie Algebras, Adv. Math., 42, 83-112 (1981) · Zbl 0476.17003
[24] Takesaki, M., Theory of Operator Algebras (1979), Springer-Verlag: Springer-Verlag New York · Zbl 0990.46034
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.