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

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

Compositio Mathematica (1977)

  • Volume: 35, Issue: 3, page 299-334
  • ISSN: 0010-437X

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Gelfand, I. M., Graev, M. I., and Verťik, A. M.. "Representations of the group of smooth mappings of a manifold X into a compact Lie group." Compositio Mathematica 35.3 (1977): 299-334. <http://eudml.org/doc/89353>.

@article{Gelfand1977,
author = {Gelfand, I. M., Graev, M. I., Verťik, A. M.},
journal = {Compositio Mathematica},
language = {eng},
number = {3},
pages = {299-334},
publisher = {Noordhoff International Publishing},
title = {Representations of the group of smooth mappings of a manifold X into a compact Lie group},
url = {http://eudml.org/doc/89353},
volume = {35},
year = {1977},
}

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
PB - Noordhoff International Publishing
VL - 35
IS - 3
SP - 299
EP - 334
LA - eng
UR - http://eudml.org/doc/89353
ER -

References

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  1. [1] S. Albeverio, R. Hoegh-Krohn: The Energy Representation of Sobolev-Lie Groups. Universität Bielefeld, 1976. Zbl0393.22013
  2. [2] H. Araki: Factorisable representations of current algebra. Publ. of RIMS., Kyoto Univ., Ser. A., 5, no. 3 (1970) 361. Zbl0238.22014MR263326
  3. [3] S. Coleman, D. Gross, R. Jackiw: Fermion avatars of the Sugawara Model. Phys. Rev., 180, no. 5 (1969) 1359. 
  4. [4] N. Dunford and J.T. Schwartz: Linear Operators, Part 1: General Theory. Interscience Publ., N.-Y; 1958. Zbl0084.10402MR117523
  5. [5] P. Delorme: 1-Cohomologie des Groupes localement compacts et Produits tensoriels continus de Representations. These de 3° cicle, Paris, 1975. MR457630
  6. [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. Zbl0233.20016
  7. [7] I.M. Gelfand, N.Ya. Vilenkin: Generalized functions, Vol. 4: Applications of Harmonic Analysis. Academic Press, New York, 1964. Zbl0136.11201MR173945
  8. [8] A. Guichardet: Symmetric Hilbert spaces and related topics. Lect. Notes in Math., no. 261, Springer, Berlin, 1972. Zbl0265.43008MR493402
  9. [9] A. Guichardet: Cogomologie des groupes localement compacts et produits tensoriels continus de representations. Paris, 1975 (preprint). Zbl0324.60005MR425005
  10. [10] A. Guichardet: Representations de GX selon Gelfand et Delorme. Séminare Bourbaki, 28-e année 1975/76, no. 486 (1976). Zbl0344.22008
  11. [11] R.S. Ismagilov: On unitary representations of the group C∞ 0(X, G), G = SU2: Mat. Sbornik, 100, no. 1 (1976) 117. Zbl0383.22002
  12. [12] K. Ito: Multiple Wiener integral. J. Math. Soc. Japan, 3 (1951) 157. Zbl0044.12202MR44064
  13. [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. Zbl0237.43005MR622034
  14. [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. Zbl0332.43009MR419688
  15. [15] A.V. Skorohod: Integration in a Hilbert Spaces. Moscow, "Nauka", 1975 (Russian). 
  16. [16] S.L. Sobolev: Some Applications of the Functional Analysis in Mathematical Physics. Leningrad, 1950 (Russian). Zbl0123.09003
  17. [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. [18] H. Sugawara: A field theory of currents. Phys. Rev.170, no. 5 (1968) 1659. 
  19. [19] A.M. Veršik: On the theory of normal dynamic systems. Doklady Acad. Nauk USSR, 144, no. 1 (1962) 9. Zbl0197.39401
  20. [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. Zbl0297.22003MR393337
  21. [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. Zbl0299.22004MR348032
  22. [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. Zbl0337.58003MR399343
  23. [23] N. Wiener: Nonlinear Problems in Random Theory. Wiley, N.-Y, 1958. Zbl0121.12302MR100912

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