Representations of the group of functions taking values in a compact Lie group

I. M. Gelfand; M. I. Graev; A. M. Veršik

Compositio Mathematica (1980)

  • Volume: 42, Issue: 2, page 217-243
  • ISSN: 0010-437X

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Gelfand, I. M., Graev, M. I., and Veršik, A. M.. "Representations of the group of functions taking values in a compact Lie group." Compositio Mathematica 42.2 (1980): 217-243. <http://eudml.org/doc/89477>.

@article{Gelfand1980,
author = {Gelfand, I. M., Graev, M. I., Veršik, A. M.},
journal = {Compositio Mathematica},
keywords = {smooth functions; Riemannian manifold; compact semi-simple Lie group; gauge group; Fourier transforms},
language = {eng},
number = {2},
pages = {217-243},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {Representations of the group of functions taking values in a compact Lie group},
url = {http://eudml.org/doc/89477},
volume = {42},
year = {1980},
}

TY - JOUR
AU - Gelfand, I. M.
AU - Graev, M. I.
AU - Veršik, A. M.
TI - Representations of the group of functions taking values in a compact Lie group
JO - Compositio Mathematica
PY - 1980
PB - Sijthoff et Noordhoff International Publishers
VL - 42
IS - 2
SP - 217
EP - 243
LA - eng
KW - smooth functions; Riemannian manifold; compact semi-simple Lie group; gauge group; Fourier transforms
UR - http://eudml.org/doc/89477
ER -

References

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  2. [2] A.M. Veršik, I.M. Gelfand and M.I. Graev: Irreducible representations of the group GX and cohomology. Funct. Anal. and its Appl.8, no 2 (1974) 67. Zbl0299.22004MR348032
  3. [3] I.M. Gelfand, M.I. Graev, A.M. Veršik: Representations of the group of smooth mappings of a manifold X into a compact Lie group. Compositio Math. 35, Fasc. 3 (1977) 299. Zbl0368.53034MR578652
  4. [4] I.M. Gelfand, N. Ya. Vilenkin: Generalized functions, Vol. 4: Applications of Harmonic Analysis. Academic Press, New York, 1964. Zbl0136.11201MR173945
  5. [5] K. Maurin: Metody przestreni Hilberta. Warsawa, 1959. MR131148
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  8. [8] R. Courant: Partial differential equations. New York, 1962. 
  9. [9] B. Simon: The P (ϕ2) Euclidean (quantum) field theory. Princeton Univ. Press, 1974. Zbl1175.81146
  10. [10] A.V. Skorohod: Integration in Hilbert spaces. Moscow, "Nauka", 1975. 
  11. [11] S.L. Sobolev: Some Applications of the Functional Analysis in Mathematical Physics. Leningrad, 1950. Zbl0123.09003
  12. [12] L. Hormander: The spectral function of an elliptic operator. Acta Math.121, no. 3-4 (1968) 193. Zbl0164.13201MR609014
  13. [13] G.E. Shilov, Fan Dik-Tin: Integral, Measure, and Derivative on linear spaces. Moscow, "Nauka", 1967. MR225964
  14. [14] M.A. Shubin: Pseudodifferential Operators and the Spectral Theory. Moscow, "Nauka", 1978. Zbl0451.47064MR509034
  15. [15] S. Albeverio, R. Hoegh-Krohn: The Energy representation of Sobolev-Lie groups. Preprint Universitat Bielefeld, 1976. Zbl0393.22013
  16. [16] A. Guichardet: Symmetric Hilbert spaces and related topics. Lect. Notes in Math. N 261, Springer, Berlin, 1972. Zbl0265.43008MR493402
  17. [17] K.R. Parthasarathy and K. Schmidt: A new method for constructing factorisable representation for current groups and current algebras, Commun. Math. Phys., 51, no. 1 (1976) 1. Zbl0332.43009MR419688

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