This article is cited in 12 papers

Measures on diffeomorphism groups for non-Archimedean manifolds: Group representations and their applications

S. V. Lyudkovskii

General Physics Institute named after A. M. Prokhorov, Russian Academy of Sciences

Abstract: Nondegenerate $\sigma$-additive measures with ranges in $\mathbb R$ and $\mathbb Q_q$ ($q\ne p$ are prime numbers) that are quasi-invariant and pseudodifferentiable with respect to dense subgroups $G'$ are constructed on diffeomorphism and homeomorphism groups $G$ for separable non-Archimedean Banach manifolds $M$ over a local field $\mathbb K$, $\mathbb K\supset\mathbb Q_p$, where $\mathbb Q_p$ is the field of $p$-adic numbers. These measures and the associated irreducible representations are used in the non-Archimedean gravitation theory.

Received: 18.06.1998
Revised: 10.02.1999

DOI: 10.4213/tmf746

 English version: Theoretical and Mathematical Physics, 1999, 119:3, 698–711

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