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Quasi-invariant measures on non-Archimedean groups and semigroups of loops and paths, their representations. II

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Quasi-invariant measures on non-Archimedean groups and semigroups of loops and paths, their representations. II ANNALES MATHÉMATIQUES BLAISE PASCAL SERGEY V. LUDKOVSKY Quasi-invariant measures on non-Archimedean groups and semigroups of loops and paths, their representations. II Annales mathématiques Blaise Pascal, tome 7, no 2 (2000), p. 55-80. <http://www.numdam.org/item?id=AMBP_2000__7_2_55_0> © Annales mathématiques Blaise Pascal, 2000, tous droits réservés. L’accès aux archives de la revue « Annales mathématiques Blaise Pascal » (http:// math.univ-bpclermont.fr/ambp/), implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Quasi-invariant measures on non-Archimedean groups and semigroups of loops and paths, their representations. II. Sergey V. Ludkovsky Ann. Math. Blaise Pascal, Vol. 7, N° 2, 2000, pp 55-80 permanent address: Theoretical Department, Institute of General Physics, Str. Vavilov 38, Moscow, 117942, Russia. Abstract Loop groups G as families of mappings of one non-Archimedean Banach manifold M into another N with marked points over the same locally compact field K of characteristic char(K) = 0 are considered. Quasi-invariant measures on them are constructed. Then measures are used to investigate irreducible representations of such groups. 1 Introduction. In the first part results on loop semigroups were exposed. This part is devoted to loop and path groups, quasi-invariant measures on them and their unitary representations. Results from Part I are used below (see also Introduction of Part I). . Irreducible components of strongly continuous unitary representations of Abelian locally compact groups a

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