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Search: MSC category 22E40 ( Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx] )

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1. CMB Online first

Cao, Wensheng; Huang, Xiaolin
A note on quaternionic hyperbolic ideal triangle groups
In this paper, the quaternionic hyperbolic ideal triangle groups are parameterized by a real one-parameter family $\{\phi_s: s\in \mathbb{R}\}$. The indexing parameter $s$ is the tangent of the quaternionic angular invariant of a triple of points in $\partial \mathbf{H}_{\mathbb{h}}^2 $ forming this ideal triangle. We show that if $s \gt \sqrt{125/3}$ then $\phi_s$ is not a discrete embedding, and if $s \leq \sqrt{35}$ then $\phi_s$ is a discrete embedding.

Keywords:quaternionic inversion, ideal triangle group, quaternionic Cartan angular invariant
Categories:20F67, 22E40, 30F40

2. CMB 2012 (vol 56 pp. 881)

Xie, BaoHua; Wang, JieYan; Jiang, YuePing
Free Groups Generated by Two Heisenberg Translations
In this paper, we will discuss the groups generated by two Heisenberg translations of $\mathbf{PU}(2,1)$ and determine when they are free.

Keywords:free group, Heisenberg group, complex triangle group
Categories:30F40, 22E40, 20H10

3. CMB 2004 (vol 47 pp. 439)

Parker, John R.
On the Stable Basin Theorem
The stable basin theorem was introduced by Basmajian and Miner as a key step in their necessary condition for the discreteness of a non-elementary group of complex hyperbolic isometries. In this paper we improve several of Basmajian and Miner's key estimates and so give a substantial improvement on the main inequality in the stable basin theorem.

Categories:22E40, 20H10, 57S30

4. CMB 2001 (vol 44 pp. 408)

Falbel, E.
Finite Groups Generated by Involutions on Lagrangian Planes of $\mathbf{C}^2$
We classify finite subgroups of $\SO(4)$ generated by anti-unitary involutions. They correspond to involutions fixing pointwise a Lagrangian plane. Explicit descriptions of the finite groups and the configurations of Lagrangian planes are obtained.

Categories:22E40, 53D99

5. CMB 1997 (vol 40 pp. 72)

Lee, Min Ho
Generalized Siegel modular forms and cohomology of locally symmetric varieties
We generalize Siegel modular forms and construct an exact sequence for the cohomology of locally symmetric varieties which plays the role of the Eichler-Shimura isomorphism for such generalized Siegel modular forms.

Categories:11F46, 11F75, 22E40

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