Irreducible unitary representations of non-Archimedean groups of diffeomorphisms
type: Item
instance of: scholarly article
title: Irreducible unitary representations of non-Archimedean groups of diffeomorphisms
zbMATH Open document ID: 0933.43003
published in: Southeast Asian Bulletin of Mathematics
publication date: 2000-03-27T00:00:00Z
review text: \(K\) 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.
Mathematics Subject Classification ID: 43A65
Mathematics Subject Classification ID: 46S10
zbMATH DE Number: 1350753
zbMATH Keywords: groups of diffeomorphisms
zbMATH Keywords: unitary representations
zbMATH Keywords: non-archimedean Banach spaces
zbMATH Keywords: complex unitary representations
zbMATH Keywords: linear isometric operators
author: Sergey V. Ludkovsky
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1350753