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Finite presentations of hyperbolic Kac-Moody groups
(Rutgers University & IHÉS)
Amphithéâtre Léon Motchane (IHES)
Amphithéâtre Léon Motchane
Le Bois Marie
35, route de Chartres
Tits defined Kac-Moody groups over commutative rings, providing infinite dimensional analogues of the Chevalley-Demazure group schemes. Tits' presentation can be simplified considerably when the Dynkin diagram is hyperbolic and simply laced. Over finitely generated rings R, we give finitely many generators and defining relations parametrized over R and we describe a further simplification for R = Z. We highlight the role of the group E10(R), conjectured to play a role in the unification of superstring theories.