arXiv subjects

Dave Witte

Publications and source records attributed to Dave Witte.

21 records · Page 2Linked to original sources

arXiv1996

Correction to "Measurable quotients of unipotent translations on homogeneous spaces

The statements of Main~Theorem~1.1 and Theorem~2.1 of the author's paper [\emph{Trans.\ Amer.\ Math.\ Soc.}\ {\bf 345} (1994) 577--594] should assume that $Γ$~is discrete and $G$~is connected. (Cors.~1.3, 5.6, and~5.8 are affected similarly.) These restrictions can be removed if the conclusions of the results are weakened to allow for the possible existence of transitive, proper subgroups of~$G$. In this form, the results can be extended to the setting where $G$ is a product of real and $p$-adic Lie groups.

math.RT↗

arXiv1996

Superrigid subgroups of solvable Lie groups

Let $Γ$ be a discrete subgroup of a simply connected, solvable Lie group~$G$, such that $\Ad_GΓ$ has the same Zariski closure as $\Ad G$. If $α\colon Γ\to \GL_n(\real)$ is any finite-dimensional representation of~$Γ$,we show that $α$ virtually extends to a continuous representation~$σ$ of~$G$. Furthermore, the image of~$σ$ is contained in the Zariski closure of the image of~$α$. When $Γ$ is not discrete, the same conclusions are true if we make the additional assumption that the closure of $[Γ, Γ]$ is a finite-index subgroup of $[G,G] \cap Γ$ (and $Γ$ is closed and $α$ is continuous).

math.RT↗

arXiv1996

Correction to "Zero-entropy affine maps on homogeneous spaces

Proposition~6.4 of the author's paper {\origpaper} is incorrect. This invalid proposition was used in the proof of Corollary~6.5, so we provide a new proof of the latter result.

math.RT↗