JournalsjemsVol. 23, No. 6pp. 2127–2151

Sum-product for real Lie groups

  • Weikun He

    Korea Institute for Advanced Study, Seoul, Republic of Korea
  • Nicolas de Saxcé

    Université Paris 13, Villetaneuse, France
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Abstract

We prove a discretized sum-product theorem for representations of Lie groups whose Jordan–Hölder decomposition does not contain the trivial representation. This expansion result is used to derive a product theorem in perfect Lie groups.

Cite this article

Weikun He, Nicolas de Saxcé, Sum-product for real Lie groups. J. Eur. Math. Soc. 23 (2021), no. 6, pp. 2127–2151

DOI 10.4171/JEMS/1052