Entropy and domination for quasi-Hitchin representations
Abstract
Let S be a closed oriented surface of genus g≥ 2. We consider an n-pleated representation ρ: π1(S) → PSLn(ℂ) obtained by bending a Hitchin representation ρ0:π1(S) → PSLn(ℝ) along a maximal geodesic lamination. The space of such n-pleated representations was recently introduced by Maloni-Martone-Mazzoli-Zhang who provided a parametrization via shear-bend cocycles. Our main result is that ρ0 dominates ρ in the Hilbert length spectrum and the translation-length spectrum, with a strict domination for most curves, that we call statistical domination. Using this, we prove some entropy rigidity results: namely, the Hilbert entropy of any quasi-Hitchin representation in the bending fiber is strictly greater than that of ρ0, the same for the translation length entropy when ρ0 is n-Fuchsian, and in the latter case a new proof that for hyperconvex representations the Hausdorff dimension of the full limit set increases. The proof involves analyzing the weighted planar networks for finite approximants of the monodromy matrix, and establishing a strict matrix domination for generic monodromy using the equidistribution of closed geodesics in the unit tangent bundle of S.
Related
- Length-convexity and domination for Hitchin representations
- Non-Hitchin Borel Anosov representations from surface groups to SL3kℝ
- On Line-Hyperplane Structures for Hitchin Representations
- GNS-like representations of a quasi *-algebra in Krein spaces
- Non-maximal quasi-isometric PU2,n+1-representations via alternating surfaces in complex pseudo-hyperbolic spaces
BibTeX
@misc{barman2026entropy,
title = {{Entropy and domination for quasi-Hitchin representations}},
author = {Pabitra Barman and Subhojoy Gupta},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.27939},
eprint = {2608.27939},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27939},
}
RIS
TY - UNPB
TI - Entropy and domination for quasi-Hitchin representations
AU - Pabitra Barman
AU - Subhojoy Gupta
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2608.27939
UR - https://arxiv.org/abs/2608.27939
AB - Let S be a closed oriented surface of genus g≥ 2. We consider an n-pleated representation ρ: π_1(S) → PSL_n(ℂ) obtained by bending a Hitchin representation ρ_0:π_1(S) → PSL_n(ℝ) along a maximal geodesic lamination. The space of such n-pleated representations was recently introduced by Maloni-Martone-Mazzoli-Zhang who provided a parametrization via shear-bend cocycles. Our main result is that ρ_0 dominates ρ in the Hilbert length spectrum and the translation-length spectrum, with a strict domination for most curves, that we call statistical domination. Using this, we prove some entropy rigidity results: namely, the Hilbert entropy of any quasi-Hitchin representation in the bending fiber is strictly greater than that of ρ_0, the same for the translation length entropy when ρ_0 is n-Fuchsian, and in the latter case a new proof that for hyperconvex representations the Hausdorff dimension of the full limit set increases. The proof involves analyzing the weighted planar networks for finite approximants of the monodromy matrix, and establishing a strict matrix domination for generic monodromy using the equidistribution of closed geodesics in the unit tangent bundle of S.
ER -