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

2018/04/07 by Giuseppe Martone, Martone, Giuseppe
Mathematics · #Geometric and Algebraic Topology #Mathematics and Applications #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1804.02587

Abstract

Parreau compactified the Hitchin component of a closed surface S of\nnegative Euler characteristic in such a way that a boundary point corresponds\nto the projectivized length spectrum of an action of \π₁(S) on an mathbb\nR-Euclidean building. In this paper, we use the positivity properties of\nHitchin representations introduced by Fock and Goncharov to explicitly describe\nthe geometry of a preferred collection of apartments in the limiting building.\n

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