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Journal Articles Journal of Differential Geometry Year : 2023

Infinitesimal Zariski closures of positive representations

Abstract

We classify the (semi-simple parts of the) Lie algebra of the Zariski closure of a discrete subgroup of a split simple real-algebraic Lie group, whose limit sets are minimal and such that the limit set in the space of full flags contains a positive triple of flags (as in Lusztig). We then apply our result to obtain a new proof of Guichard's classification of Zariski closures of Hitchin representations into $PSL_d(\mathbb{R}).$

Dates and versions

hal-03100597 , version 1 (06-01-2021)

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Andrés Sambarino. Infinitesimal Zariski closures of positive representations. Journal of Differential Geometry, In press. ⟨hal-03100597⟩
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