Corpus ID: 118706052

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

@article{Gelfand1977RepresentationsOT,
  title={Representations of the group of smooth mappings of a manifold X into a compact Lie group},
  author={Izrail Moiseevich Gel'fand and Mark Iosifovich Graev and A. M. Verťik},
  journal={Compositio Mathematica},
  year={1977},
  volume={35},
  pages={299-334}
}
Some important nonlocal representations of the group Gx consisting of C°°-mappings of a Riemannian manifold X to a compact semisimple Lie group G are constructed. The irreducibility, as well as non-equivalence of the introduced representations corresponding to different Riemannian metrics are proved. The ring of representations is calculated. COMPOSITIO MATHEMATICA, Vol. 35, Fasc. 3, 1977, pag. 299-334 Noordhoff International Publishing Printed in the Netherlands 
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References

SHOWING 1-10 OF 18 REFERENCES
REPRESENTATIONS OF THE GROUP OF DIFFEOMORPHISMS
This article contains a survey of results on representations of the diffeomorphism group of a noncompact manifold X associated with the space ΓX of configurations (that is, of locally finite subsets)Expand
REPRESENTATIONS OF THE GROUP SL(2, R), WHERE R IS A RING OF FUNCTIONS
We obtain a construction of the irreducible unitary representations of the group of continuous transformations , where is a compact space with a measure and , that commute with transformations inExpand
ON UNITARY REPRESENTATIONS OF THE GROUP $ C_0^\infty (X, G)$, $ G = SU_2$
In this paper a family of irreducible unitary representations of the group is constructed, where is an open set in , . The group consists of all infinitely differentiable mappings with compactExpand
A new method for constructing factorisable representations for current groups and current algebras
LetCe∞(Rn,G) denote the group of infinitely differentiable maps fromn-dimensional Euclidean space into a simply connected and connected Lie group, which have compact support. This paper introduces aExpand
Cohomologie des groupes localement compacts et produits tensoriels continus de représentations
The following is an expository paper, containing few and sometimes incomplete proofs, on continuous tensor products of Hilbert spaces and of group representations, and on the irreducibility of theExpand
Positive Definite Kernels, Continuous Tensor Products, and Central Limit Theorems of Probability Theory
Positive definite kernels and continuous tensor products.- Limit theorems for uniformly infinitesimal families of positive definite kernels.- The analysis of cocycles of first order on some specialExpand
Symmetric Hilbert spaces and related topics
The first € price and the £ and $ price are net prices, subject to local VAT. Prices indicated with * include VAT for books; the €(D) includes 7% for Germany, the €(A) includes 10% for Austria.Expand
Nonlinear Problems in Random Theory
A series of lectures on the role of nonlinear processes in physics, mathematics, electrical engineering, physiology, and communication theory.From the preface:"For some time I have been interested inExpand
GRAEV: Irreducible representations of the group GX and cogomology
  • Funct. Anal. and its Appl. 8,
  • 1974
Integration in Hilbert Space
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