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Isomorphisms of Kac-Moody groups which preserve bounded subgroups

P. -E. Caprace·B. Muehlherr
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Abstract

A subgroup of a Kac-Moody group is called bounded if it is contained in the intersection of two finite type parabolic subgroups of opposite signs. In this paper, we study the isomorphisms between Kac-Moody groups over arbitrary fields of cardinality at least 4, which preserve the set of bounded subgroups. We show that such an isomorphism between two such Kac-Moody groups induces an isomorphism between the respective twin root data of these groups. As a consequence, we obtain the solution of the isomorphism problem for Kac-Moody groups over finite fields of cardinality at least 4.

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P. -E. Caprace, B. Muehlherr. 2005-06-27. Isomorphisms of Kac-Moody groups which preserve bounded subgroups. https://doi.org/10.1016/j.aim.2005.08.008

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