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MiS Preprint
32/2003

Proof of a Conjecture by Lewandowski and Thiemann

Christian Fleischhack

Abstract

It is proven that for compact, connected and semisimple structure groups every degenerate labelled web is strongly degenerate. This conjecture by Lewandowski and Thiemann implies that diffeomorphism invariant operators in the category of piecewise smooth immersive paths preserve the decomposition of the space of integrable functions w.r.t. the degeneracy and symmetry of the underlying labelled webs. This property is necessary for lifting these operators to well-defined operators on the space of diffeomorphism invariant states.

Received:
Mar 31, 2003
Published:
Mar 31, 2003
MSC Codes:
47A15, 47A05, 81T13, 58D20, 83C45

Related publications

inJournal
2004 Repository Open Access
Christian Fleischhack

Proof of a conjecture by Lewandowski and Thiemann

In: Communications in mathematical physics, 249 (2004) 2, pp. 331-352