Seminar Algebra and Geometry: Bruno Duchesne (The Hebrew University of Jerusalem)

Infinite-dimensional non-positively curved symmetric spaces of finite rank

Symmetric spaces of non-compact type (which are simply-connected Riemannian manifolds of non-positive curvature with a geodesic symmetry at each point) are classical and useful geometric tools to understand finite-dimensional linear representations of groups.

We will look at some infinite dimensional symmetric spaces of non-positive curvature which have a remarkable property : they have finite rank. There exists a positive integer p such that any isometrically embedded Euclidean space has dimension at most p.

The talk will be focused on the properties of these spaces and some group actions which come from (non-unitary) infinite-dimensional representations.

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