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Primitive stable representations in higher rank semisimple Lie groups

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Abstract

We study primitive stable representations of free groups into higher rank semisimple Lie groups and their properties. Let \(\Sigma \) be a compact, connected, orientable surface (possibly with boundary) of negative Euler characteristic. We first verify \(\sigma _{mod}\)-regularity for convex projective structures and positive representations. Then we show that the holonomies of convex projective structures and positive representations on \(\Sigma \) are all primitive stable if \(\Sigma \) has one boundary component.

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Authors and Affiliations

  1. School of Mathematics, Korea Institute for Advanced Study, Hoegiro 85, Dongdaemun-gu, Seoul, 02455, Republic of Korea

    Inkang Kim

  2. Department of Mathematics, Jeju National University, 102 Jejudaehak-ro, Jeju, 63243, Republic of Korea

    Sungwoon Kim

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  1. Inkang Kim
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  2. Sungwoon Kim
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I. Kim gratefully acknowledges the partial support of Grant (NRF-2017R1A2A2A05001002) and KIAS Individual Grant (MG031408), and a warm support of UC Berkeley during his stay. S. Kim gratefully acknowledges supports from the 2020 scientific promotion program by Jeju National University and the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (NRF-2015R1D1A1A09058742).

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Kim, I., Kim, S. Primitive stable representations in higher rank semisimple Lie groups. Rev Mat Complut 34, 715–745 (2021). https://doi.org/10.1007/s13163-020-00372-w

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