Transforming the Cayley transform
10th December, 2009. Seminaire des Thésards, Institut de Mathématiques de Jussieu, Paris.
Organized by Paloma Bengoechea, Luc Deléaval, Simone Diverio, Banafsheh Farang-Hariri, Benjamin Wagener and Maxime Wolff.
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In this talk we will discuss, in a very naïve way, different versions of the Cayley transform:
- The original version for matrices as appeared in a paper by Arthur Cayley in 1846.
- The geometric version between the Poincaré disk and the Poincaré half-plane.
- Its generalization to bounded symmetric domains and generalized half-planes.
- The role played in the classification of real semisimple Lie algebras.
- And the generalized Cayley correspondence in the recent theory of G-Higgs bundles.