Positive configurations of flags in a building and limits of positive representations

Giuseppe Martone

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arXiv · 1804.02587

Positive configurations of flags in a building and limits of positive representations

Giuseppe Martone

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Abstract

Parreau compactified the Hitchin component of a closed surface $S$ of negative Euler characteristic in such a way that a boundary point corresponds to the projectivized length spectrum of an action of $\pi_1(S)$ on an $\mathbb R$-Euclidean building. In this paper, we use the positivity properties of Hitchin representations introduced by Fock and Goncharov to explicitly describe the geometry of a preferred collection of apartments in the limiting building.

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Giuseppe Martone. 2018-04-07. Positive configurations of flags in a building and limits of positive representations. https://arxiv.org/abs/1804.02587

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