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<p>In this paper, we study the interaction between the totally positive monoid <i>G</i><sub>⩾0</sub> attached to a connected reductive group <i>G</i> with a pinning and the conjugacy classes in <i>G</i>. In particular, we study how a conjugacy class meets the various cells of <i>G</i><sub>⩾0</sub>. We also state a conjectural Jordan decomposition for <i>G</i><sub>⩾0</sub> and prove it in some special cases.</p>

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Total positivity and conjugacy classes

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • Xuhua He,
  • George Lusztig

摘要

In this paper, we study the interaction between the totally positive monoid G⩾0 attached to a connected reductive group G with a pinning and the conjugacy classes in G. In particular, we study how a conjugacy class meets the various cells of G⩾0. We also state a conjectural Jordan decomposition for G⩾0 and prove it in some special cases.