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<p>We study the quasi-admissibility and raisability of some nilpotent orbits of a covering group. In particular, we determine the degree of the cover such that a given split nilpotent orbit is quasi-admissible and non-raisable. The speculated wavefront sets of theta representations are also computed explicitly and are shown to be quasi-admissible and non-raisable. Lastly, we determine the leading coefficients in the Harish-Chandra character expansion of the theta representations of covers of the general linear groups.</p>

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Quasi-admissible, raisable nilpotent orbits, and theta representations

  • 期刊论文

  • 发表日期：

    2025年3月25日

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  • Fan Gao,
  • Baiying Liu,
  • Wan-Yu Tsai

摘要

We study the quasi-admissibility and raisability of some nilpotent orbits of a covering group. In particular, we determine the degree of the cover such that a given split nilpotent orbit is quasi-admissible and non-raisable. The speculated wavefront sets of theta representations are also computed explicitly and are shown to be quasi-admissible and non-raisable. Lastly, we determine the leading coefficients in the Harish-Chandra character expansion of the theta representations of covers of the general linear groups.