Representation equivalent Bieberbach groups and strongly isospectral flat manifolds

LAURET, EMILIO AGUSTÍN

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES

CANADIAN MATHEMATICAL SOC

Lugar: Vancouver; Año: 2014 vol. 57 p. 357 - 363

0008-4395

Let $Gamma_1$ and $Gamma_2$ be Bieberbach groups contained in the full isometry group $G$ of $mathbb{R}^n$. We prove that if the compact flat manifolds $Gamma_1ackslashmathbb{R}^n$ and $Gamma_2ackslashmathbb{R}^n$ are strongly isospectral then the Bieberbach groups $Gamma_1$ and $Gamma_2$ are representation equivalent, that is, the right regular representations $L^2(Gamma_1ackslash G)$ and $L^2(Gamma_2ackslash G)$ are unitarily equivalent.