Irreducible unitary representations of non-Archimedean groups of diffeomorphisms
\(K\) denotes a finite extension of \({\mathbb Q}_p\). Let \(M\) be a Banach manifold over \(K\) with a countable atlas. Two groups of diffeomorphisms of \(M\) are defined, one of them is written as \(GC(t,M)\). In the paper irreducible complex unitary representations of \(GC(t,M)\) are constructed. For a certain non-archimedean Banach space \(\overline{H}\) over \(K\), one also constructs irreducible representations of \(GC(t,M)\) as linear isometric operators on \(\overline{H}\). We note that the topological group \(GC(t,M)\) is very large and that the representations are infinite dimensional. The reviewer is unable to relate the two types of representations with better known infinite dimensional representations, e.g., the automorphic representations of the Langlands program.
scientific article; zbMATH DE number 1350753