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Volume invariant and maximal representations of discrete subgroups of Lie groups

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Abstract

Let \(\Gamma \) be a lattice in a connected semisimple Lie group \(G\) with trivial center and no compact factors. We introduce a volume invariant for representations of \(\Gamma \) into \(G\), which generalizes the volume invariant for representations of uniform lattices introduced by Goldman. Then, we show that the maximality of this volume invariant exactly characterizes discrete, faithful representations of \(\Gamma \) into \(G\).

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Authors and Affiliations

  1. School of Mathematics, KIAS, Hoegiro 85, Dongdaemun-gu, Seoul, 130-722, Republic of Korea

    Sungwoon Kim & Inkang Kim

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  1. Sungwoon Kim
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  2. Inkang Kim
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Correspondence to Inkang Kim.

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The second author gratefully acknowledges the partial support of NRF Grant (2010-0024171)

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Kim, S., Kim, I. Volume invariant and maximal representations of discrete subgroups of Lie groups. Math. Z. 276, 1189–1213 (2014). https://doi.org/10.1007/s00209-013-1241-y

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  • DOI: https://doi.org/10.1007/s00209-013-1241-y

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