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Prerequisites: Lie Groups I, Lie Groups II (Symmetric Spaces).
Contents: Symmetric spaces of non-compact type: Roots and root systems. Characterizations of the Weyl group and its action on the Weyl chambers. Geometric boundary and its characterization via Busemann functions. The space SL(n,R)/SO(n) and the Imbedding Theorem. Geometric Iwasawa decomposition. Tits metric on the geometric boundary.
Organizers: Prof. Dr. Marc Burger, Stephan Tornier.
The seminar takes place on Thursdays, 1 p.m. to 4 p.m. at HG D3.2, until 13.11.2014.
Date | Speaker | Contents |
18.09.2014 | Stephan Tornier |
Introduction, discussion of possible topics and distribution of talks. |
25.09.2014 | Matteo Felder | Root systems of symmetric spaces of non-compact type. Equivalence of several definitions of the Weyl group. |
02.10.2014 | Stephan Tornier |
Abstract root systems. The Weyl group acts simply transitively on the set of Weyl chambers. |
09.10.2014 | Pascal Wild |
Geometric boundary of a symmetric space of non-compact type. Equivalent characterization via Busemann functions. |
16.10.2014 | Leyli Mammadova |
Explicit description of the example SL(n,R)/SO(n). A sketch of the Imbedding Theorem. |
23.10.2014 | Giuliano Basso |
Parabolic subgroups: Preparations for the Iwasawa decomposition. |
30.10.2014 | Andreas Wieser |
Proof of the Iwasawa decomposition. Illustrations in the case SL(n,R)/SO(n). |
06.11.2014 | Raphael Schumacher |
Iwasawa decomposition on the level of Lie algebras. Angular metric and Tits metric on the geometric boundary. |
13.11.2014 | Stephan Tornier | Towards the Tits Building, abstract buildings. |
Werner Ballmann: Lectures on spaces of nonpositive curvature.
Armand Borel: Semisimple groups and Riemannian symmetric spaces.
Martin Bridson and André Haefliger: Metric spaces of non-positive curvature.
Patrick B. Eberlein: Geometry of nonpositively curved manifolds.
Patrick B. Eberlein: Structure of manifolds of nonpositive curvature.
Sigurdur Helgason: Differential Geometry, Lie Groups, and Symmetric Spaces.
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