Abstract:Let $G_\mathbb R$ be a real form of a complex, semisimple Lie group $G$. Assume $G_\mathbb R$ has holomorphic discrete series. Let $\mathcal W$ be a nilpotent coadjoint $G_\mathbb R$-orbit contained in the wave front set of a holomorphic discrete series. We prove a limit formula, expressing the canonical measure on $\mathcal W$ as a limit of canonical measures on semisimple coadjoint orbits, where the parameter of orbits varies over the positive chamber defined by the Borel subalgebra associated with holomorphic discrete series.

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中文翻译：

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与全纯离散级数相关的幂零轨道的不变测度

摘要：令$G_\mathbb R$ 是复半单李群$G$ 的实数形式。假设 $G_\mathbb R$ 具有全纯离散级数。令 $\mathcal W$ 是一个幂零共伴随 $G_\mathbb R$ 轨道，包含在全纯离散级数的波前集中。我们证明了一个极限公式，将 $\mathcal W$ 上的规范测度表示为半单共伴轨道上的规范测度的极限，其中轨道参数在与全纯离散级数相关的 Borel 子代数定义的正室上变化。

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