# 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

#### 37 Citations

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A class of unitary representations of the group of maps from a Riemannian manifold to a compact semisimple Lie group which are a modification of the so‐called energy representations is considered.… Expand

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Construction of Quasi Invariant Probability Measures on Some Current Groups of Continuous Sections of a Bundle of Compact Semisimple Lie Groups

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a) In the seventies, several papers of A.M. Vershik, I.M. Gelfand and M.I. Graev ([19], [20], [21]) initiated the research of non located continuous irreducible unitary representations of current… Expand

Generalized energy representations for current groups

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Abstract The class of energy representations of the group D ( X , G ) of compactly supported smooth mappings from a manifold X into a compact semisimple Lie group G is substantially enlarged in the… Expand

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We consider the energy representation for the gauge group. The gauge group is the set of C∞-mappings from a compact Riemannian manifold to a semi-simple compact Lie group. In this paper, we obtain… Expand

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Let Γ.A be the semi-direct product group of a nuclear Lie group Γ with the additive group A of a real nuclear vector space. We give an explicit description of all the continuous representations of… Expand

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