In this talk I will present a general construction in terms of Higgs bundles of the higher Teichmüller components of the character variety of a surface group for a real Lie group admitting a positive structure in the sense of Guichard-Wienhard. Key ingredients in this construction are the notion of magical sl2-triple, that we introduce, and the Cayley correspondence. Basics on Higgs bundle theory will be explained.
(Based on joint work with Bradlow, Collier, Gothen and Oliveira).
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