Abstract involutions of algebraic groups and of Kac-Moody groups

Details Abstract involutions of algebraic groups and of Kac-Moody groups Abstract involutions of algebraic groups and of Kac-Moody groups

2009-05-08

arxiv.org/abs/0905.1280v2

Mathematics

Group Theory

Scientific paper

10.1515/JGT.2010.033

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.

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