## Duke Mathematical Journal

### Rigidity of group actions on homogeneous spaces, III

#### Abstract

Consider homogeneous $G/H$ and $G/F$, for an $S$-algebraic group $G$. A lattice $\Gamma$ acts on the left strictly conservatively. The following rigidity results are obtained: morphisms, factors, and joinings defined a priori only in the measurable category are in fact algebraically constrained. Arguing in an elementary fashion, we manage to classify all the measurable $\Phi$ commuting with the $\Gamma$-action: assuming ergodicity, we find that they are algebraically defined.

#### Article information

Source
Duke Math. J., Volume 164, Number 1 (2015), 115-155.

Dates
First available in Project Euclid: 9 January 2015

https://projecteuclid.org/euclid.dmj/1420813015

Digital Object Identifier
doi:10.1215/00127094-2860021

Mathematical Reviews number (MathSciNet)
MR3299103

Zentralblatt MATH identifier
1351.37011

#### Citation

Bader, Uri; Furman, Alex; Gorodnik, Alex; Weiss, Barak. Rigidity of group actions on homogeneous spaces, III. Duke Math. J. 164 (2015), no. 1, 115--155. doi:10.1215/00127094-2860021. https://projecteuclid.org/euclid.dmj/1420813015

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