幂零群的相位恢复
Phase retrieval for nilpotent groups
摘要：
研究了幂零群的一般不可约表示的轨道、单连通李群类和有限群的相位恢复性质。通过归纳证明了在李群情形下，所有的不可约表示都可以进行相位恢复。对于有限群的情形，我们主要研究$p$ -群。这里我们的主要结果指出，任何不可约表示的任意$p$ -群的指数$p$和大小$\le p^{2+p/2}$相位恢复。尽管这两种设置之间存在根本差异，但我们的归纳证明方法非常相似。
英文摘要：
We study the phase retrieval property for orbits of general irreducible representations of nilpotent groups, for the classes of simply connected connected Lie groups, and for finite groups. We prove by induction that in the Lie group case, all irreducible representations do phase retrieval. For the finite group case, we mostly focus on $p$-groups. Here our main result states that every irreducible representation of an arbitrary $p$-group with exponent $p$ and size $\le p^{2+p/2}$ does phase retrieval. Despite the fundamental differences between the two settings, our inductive proof methods are remarkably similar.
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