JournalsggdVol. 14, No. 3pp. 1007–1022

Lattice deformations in the Heisenberg group

  • Jayadev S. Athreya

    University of Washington, Seattle, USA
  • Ioannis Konstantoulas

    Uppsala University, Sweden
Lattice deformations in the Heisenberg group cover
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Abstract

The space of deformations of the integer Heisenberg group under the action of Aut(H(R))(\mathbf H(\mathbb R)) is a homogeneous space for a non-reductive group. We analyze its structure as a measurable dynamical system and obtain mean and variance estimates for Heisenberg lattice point counting in measurable subsets of R3\mathbb R^3; in particular, we obtain a random Minkowski-type theorem. Unlike the Euclidean case, we show there are necessary geometric conditions on the sets that satisfy effective variance bounds.

Cite this article

Jayadev S. Athreya, Ioannis Konstantoulas, Lattice deformations in the Heisenberg group. Groups Geom. Dyn. 14 (2020), no. 3, pp. 1007–1022

DOI 10.4171/GGD/572