Representations of the group of smooth mappings of a manifold X into a compact Lie group

Gelfand, I. M.; Graev, M. I.; Verťik, A. M.

Gelfand, I. M. ; Graev, M. I. ; Verťik, A. M.

Compositio Mathematica, Tome 35 (1977) no. 3, pp. 299-334.

MR Zbl | 3 citations dans Numdam

@article{CM_1977__35_3_299_0,
     author = {Gelfand, I. M. and Graev, M. I. and Ver\v{t}ik, A. M.},
     title = {Representations of the group of smooth mappings of a manifold {X} into a compact {Lie} group},
     journal = {Compositio Mathematica},
     pages = {299--334},
     publisher = {Noordhoff International Publishing},
     volume = {35},
     number = {3},
     year = {1977},
     mrnumber = {578652},
     zbl = {0368.53034},
     language = {en},
     url = {http://archive.numdam.org/item/CM_1977__35_3_299_0/}
}

TY  - JOUR
AU  - Gelfand, I. M.
AU  - Graev, M. I.
AU  - Verťik, A. M.
TI  - Representations of the group of smooth mappings of a manifold X into a compact Lie group
JO  - Compositio Mathematica
PY  - 1977
SP  - 299
EP  - 334
VL  - 35
IS  - 3
PB  - Noordhoff International Publishing
UR  - http://archive.numdam.org/item/CM_1977__35_3_299_0/
LA  - en
ID  - CM_1977__35_3_299_0
ER  -

%0 Journal Article
%A Gelfand, I. M.
%A Graev, M. I.
%A Verťik, A. M.
%T Representations of the group of smooth mappings of a manifold X into a compact Lie group
%J Compositio Mathematica
%D 1977
%P 299-334
%V 35
%N 3
%I Noordhoff International Publishing
%U http://archive.numdam.org/item/CM_1977__35_3_299_0/
%G en
%F CM_1977__35_3_299_0

Gelfand, I. M.; Graev, M. I.; Verťik, A. M. Representations of the group of smooth mappings of a manifold X into a compact Lie group. Compositio Mathematica, Tome 35 (1977) no. 3, pp. 299-334. http://archive.numdam.org/item/CM_1977__35_3_299_0/

Bibliographie
Cité par

[1] S. Albeverio, R. Hoegh-Krohn: The Energy Representation of Sobolev-Lie Groups. Universität Bielefeld, 1976.

[2] H. Araki: Factorisable representations of current algebra. Publ. of RIMS., Kyoto Univ., Ser. A., 5, no. 3 (1970) 361. | MR | Zbl

[3] S. Coleman, D. Gross, R. Jackiw: Fermion avatars of the Sugawara Model. Phys. Rev., 180, no. 5 (1969) 1359.

[4] N. Dunford and J.T. Schwartz: Linear Operators, Part 1: General Theory. Interscience Publ., N.-Y; 1958. | MR | Zbl

[5] P. Delorme: 1-Cohomologie des Groupes localement compacts et Produits tensoriels continus de Representations. These de 3° cicle, Paris, 1975. | MR

[6] I.M. Gelfand, M.I. Graev: Representations of the group of quaternions over local compact and functional fields. Funct. Anal. and its Appl., 2, no. 1 (1968) 20. | Zbl

[7] I.M. Gelfand, N.Ya. Vilenkin: Generalized functions, Vol. 4: Applications of Harmonic Analysis. Academic Press, New York, 1964. | MR | Zbl

[8] A. Guichardet: Symmetric Hilbert spaces and related topics. Lect. Notes in Math., no. 261, Springer, Berlin, 1972. | MR | Zbl

[9] A. Guichardet: Cogomologie des groupes localement compacts et produits tensoriels continus de representations. Paris, 1975 (preprint).

[10] A. Guichardet: Representations de GX selon Gelfand et Delorme. Séminare Bourbaki, 28-e année 1975/76, no. 486 (1976). | Numdam | Zbl

[11] R.S. Ismagilov: On unitary representations of the group C∞ 0(X, G), G = SU2: Mat. Sbornik, 100, no. 1 (1976) 117. | Zbl

[12] K. Ito: Multiple Wiener integral. J. Math. Soc. Japan, 3 (1951) 157. | MR | Zbl

[13] K.R. Parthasarathy and K. Schmidt: Positive definite kernels, continuous tensor products and central limit theorems of probability theory. Lect. Notes in Math., no. 272, Springer, Berlin, 1972. | MR | Zbl

[14] K.R. Parthasarathy and K. Schmidt: A new method for constructing factorisable representations for current groups and current algebras. Commun. Math. Phys; 51, no. 1 (1976) 1. | MR | Zbl

[15] A.V. Skorohod: Integration in a Hilbert Spaces. Moscow, "Nauka", 1975 (Russian).

[16] S.L. Sobolev: Some Applications of the Functional Analysis in Mathematical Physics. Leningrad, 1950 (Russian).

[17] R.F. Streater: Current commutation relations, continuous tensor products and infinitely divisible group representations. Rendiconti di Sc. Int. di Fisica E. Fermi, 11 (1969) 247.

[18] H. Sugawara: A field theory of currents. Phys. Rev. 170, no. 5 (1968) 1659.

[19] A.M. Veršik: On the theory of normal dynamic systems. Doklady Acad. Nauk USSR, 144, no. 1 (1962) 9. | Zbl

[20] A.M. Veršik, I.M. Gelfand and M.I. Graev: Representations of the group SL (2, R), where R is a ring of functions. Russ. Math. Surv. 28, no. 5 (1973) 83. | MR | Zbl

[21] A.M. Veršik, I.M. Gelfand and M.I. Graev: Irreducible representations of the group GX and cogomology. Funct. Anal. and its Appl. 8, no. 2 (1974) 67. | MR | Zbl

[22] A.M. Veršik, I.M. Gelfand and M.I. Graev: Representations of the group of diffeomorphisms. Uspehi Matemat. Nauk, 30, no. 6 (1975) 3. | MR | Zbl

[23] N. Wiener: Nonlinear Problems in Random Theory. Wiley, N.-Y, 1958. | MR | Zbl