Let M be a connected differentiable manifold. Denote by Omega(m)(M) the space of H-1-loops based at a fixed point m is an element of M. Associated to Omega(m)(M) one has <(Omega)over tilde>(m)(M), the group of unparameterized loops. Given a bundle-connection pair (E, del) over M with fiber the finite-dimensional vector space V and structure group G subset of GL(V) we get (up to equivalence) a smooth representation of <(Omega)over tilde>(m)(M) in G given by the parallel transport operator P-del. It is possible to find in the literature several versions of the converse theorem, namely: all (smooth) representations of <(Omega)over tilde>(m)(M) arise in the above described way from a bundle-connection pair. It is shown in the present paper that the correct setting for this theorem is the theory of induced representations for groupoids.
Gibilisco P. (1997). Bundle-connection pairs and loop group representations. MATHEMATICAL NOTES OF THE ACADEMY OF SCIENCES OF THE USSR, 61, 417-429.
Tipologia: | Articolo su rivista |
Citazione: | Gibilisco P. (1997). Bundle-connection pairs and loop group representations. MATHEMATICAL NOTES OF THE ACADEMY OF SCIENCES OF THE USSR, 61, 417-429. |
IF: | Con Impact Factor ISI |
Lingua: | English |
Settore Scientifico Disciplinare: | Settore MAT/06 - Probabilita' e Statistica Matematica |
Revisione (peer review): | Sì, ma tipo non specificato |
Tipo: | Articolo |
Rilevanza: | Rilevanza internazionale |
Stato di pubblicazione: | Pubblicato |
Data di pubblicazione: | 1997 |
Titolo: | Bundle-connection pairs and loop group representations |
Autori: | |
Autori: | Gibilisco P. |
Appare nelle tipologie: | 01 - Articolo su rivista |
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