Abstract involutions of algebraic groups and of Kac-Moody groups

Abstract

Based on the second author's thesis in this article we provide a uniform treatment of abstract involutions of algebraic groups and of Kac-Moody groups using twin buildings, RGD systems, and twisted involutions of Coxeter groups. Notably we simultaneously generalize the double coset decompositions established by Springer and by Helminck-Wang for algebraic groups and by Kac-Wang for certain Kac-Moody groups, we analyze the filtration studied by Devillers-Muhlherr in the context of arbitrary involutions, and we answer a structural question on the combinatorics of involutions of twin buildings raised by Bennett-Gramlich-Hoffman-Shpectorov.

Cited by in corpus (8)

• On topological twin buildings and topological split Kac-Moody groups
• Infinite generation of non-cocompact lattices on right-angled buildings
• Kac-Moody symmetric spaces
• Expander graphs from Curtis Tits groups
• Lattices in complete rank 2 Kac-Moody groups
• Decompositions of Kac-Moody groups
• The combinatorics of automorphisms and opposition in generalised polygons
• Cocompact lattices in complete Kac-Moody groups with Weyl group right-angled or a free product of spherical special subgroups