Finite presentations of hyperbolic Kac-Moody groups

by Prof. Lisa CARBONE (Rutgers University & IHÉS)

Tuesday May 26, 2015, 11:45 AM → 12:45 PM Europe/Paris

Amphithéâtre Léon Motchane (IHES)

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.