Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 55, Number 1 (2015), 219-242.
Deforming discontinuous subgroups of reduced Heisenberg groups
Let be the -dimensional reduced Heisenberg group, and let be an arbitrary connected Lie subgroup of . Given any discontinuous subgroup for , we show that resulting deformation space of the natural action of on is endowed with a smooth manifold structure and is a disjoint union of open smooth manifolds. Unlike the setting of simply connected Heisenberg groups, we show that the stability property holds and that any discrete subgroup of is stable, following the notion of stability. On the other hand, a local (and hence global) rigidity theorem is obtained. That is, the related parameter space admits a rigid point if and only if is finite.
Kyoto J. Math., Volume 55, Number 1 (2015), 219-242.
First available in Project Euclid: 13 March 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 22E27: Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)
Secondary: 32G05: Deformations of complex structures [See also 13D10, 16S80, 58H10, 58H15]
Baklouti, Ali; Ghaouar, Sonia; Khlif, Fatma. Deforming discontinuous subgroups of reduced Heisenberg groups. Kyoto J. Math. 55 (2015), no. 1, 219--242. doi:10.1215/21562261-2848169. https://projecteuclid.org/euclid.kjm/1426252136