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ВИДЕОТЕКА |
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Polar actions on symmetric spaces Jürgen Berndt King's College London |
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Аннотация: An isometric action of a connected Lie group Soon afterwards an attempt was made to classify polar actions on symmetric spaces. For irreducible symmetric spaces of compact type the final step for a complete classification appears to have been just completed by Kollross using yet unpublished work of Lytchak on polar foliations. In the talk I want to focus on symmetric spaces of noncompact type. For actions of reductive groups one can use the concept of duality between symmetric spaces of compact type and of noncompact type. However, new examples and phenomena arise from the geometry induced by actions of parabolic subgroups, for which there is no analogon in the compact case. I plan to discuss the main difficulties one encounters here and some partial solutions. The only complete classification known so far has just been obtained in joint work with José Carlos Díaz-Ramos for the complex hyperbolic plane. Язык доклада: английский |