关于群生成的幂零群的单项表示
On monomial representations of finitely generated nilpotent groups
摘要：
D. Segal指出，每个复不可约表示的一个非线性生成的幂零群$G$是单性的当且仅当$G$是阿贝尔有限的。A. n. Parshin最近被I.V.Beloshapka和S. O. Gorchinskii（2016）刻画了n-生成幂零群的单项不可约表示。本文结合I. D.布朗和PC。库茨科刻画了二阶幂零群的有限维不可约表示，并给出了中心秩为1的二阶群的有限维表示的完整刻画.
英文摘要：
A result of D. Segal states that every complex irreducible representation of a finitely generated nilpotent group $G$ is monomial if and only if $G$ is abelian-by-finite. A conjecture of A. N. Parshin, recently proved affirmatively by I.V. Beloshapka and S. O. Gorchinskii (2016), characterizes the monomial irreducible representations of finitely generated nilpotent groups. This article gives a slightly shorter proof of the conjecture combining the ideas of I. D. Brown and P. C. Kutzko. We also characterize finite dimensional irreducible representations of two step nilpotent groups and also provide a full description of the finite dimensional representations of two step groups whose center has rank one.
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