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Title:
The symmetric space of type E10, and the action of the arithmetic Kac-Moody group
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Abstract:
Freyn, Hartnick, Horn and myself constructed Kac-Moody symmetric spaces of non-affine type. A recent result by Grüning and myself states that, if the Dynkin diagram does not involve the label infinity, then any Kac-Moody symmetric space is a universal object of its sub-symmetric spaces of rank 1 and 2 embedded at a common base point; in fact, this result applies to Riemannian symmetric spaces of split non-compact type as well. In a certain sense this says that complete information about the geometry of a symmetric space is already contained in its sub-symmetric spaces of rank 1 and 2.
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