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

Abstract

Loop and path groups G and semigroups S 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.