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Journal of Lie Theory 26 (2016), No. 4, 1079--1105
Copyright Heldermann Verlag 2016



Isomorphisms and Rigidity of Arithmetic Kac-Moody Groups

Amir Farahmand Parsa
Mathematisches Institut, Justus-Liebig-Universitдt, Arndtstrasse 2, 35392 Giessen, Germany
[email protected]

Max Horn
Mathematisches Institut, Justus-Liebig-Universitдt, Arndtstrasse 2, 35392 Giessen, Germany
[email protected]

Ralf Kцhl
Mathematisches Institut, Justus-Liebig-Universitдt, Arndtstrasse 2, 35392 Giessen, Germany
[email protected]



We solve the isomorphism problem for subgroups of integral points of two-spherical Kac-Moody groups over the rational numbers. Along the way we establish versions of Mostow-Margulis strong rigidity and Margulis superrigidity with target in two-spherical split Kac-Moody groups over the rational numbers for arithmetically defined subgroups.

Keywords: Arithmetic Kac-Moody group, twin building, isomorphism problem, Mostow-Margulis strong rigidity, Margulis superrigidity.

MSC: 20G44, 20G25, 51E24

[ Fulltext-pdf  (444  KB)] for subscribers only.


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Fig. 4Figure 4

Artist’s illustration of sandbox-model deformation caused by deflating an air balloon 6.5 cm across and 4.5 cm high buried under colored layers behind a plastic window. Layers were a mix of five parts sand to one part plaster of Paris powder. The pre-inflated balloon was flattened by the weight above it. As the balloon was deflated, faults propagated upward, dropping a central plug (zone 1) between reverse faults or monoclines (zone 2), followed by inward movement along peripheral normal faults in zone 3. (The balloon withdrew back from the window as it deflated.) The surface morphology mimicked similar experiments centered in the sandbox, showing that window friction had little effect. Collapse geometry was insensitive to deflation speed. A second set of reverse faults sometimes developed (see also Martí et al., 1994; Roche et al., 2000). Painted by Don Davis in 1974, idealized slightly from imperfectly parallel initial layering in sandbox experiments performed under the author’s direction.

0

Fig. 4Figure 4

Artist’s illustration of sandbox-model deformation caused by deflating an air balloon 6.5 cm across and 4.5 cm high buried under colored layers behind a plastic window. Layers were a mix of five parts sand to one part plaster of Paris powder. The pre-inflated balloon was flattened by the weight above it. As the balloon was deflated, faults propagated upward, dropping a central plug (zone 1) between reverse faults or monoclines (zone 2), followed by inward movement along peripheral normal faults in zone 3. (The balloon withdrew back from the window as it deflated.) The surface morphology mimicked similar experiments centered in the sandbox, showing that window friction had little effect. Collapse geometry was insensitive to deflation speed. A second set of reverse faults sometimes developed (see also Martí et al., 1994; Roche et al., 2000). Painted by Don Davis in 1974, idealized slightly from imperfectly parallel initial layering in sandbox experiments performed under the author’s direction.

4
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