Irreducible representations of finitely generated nilpotent groups

被引：3

作者：

Beloshapka, I. V. ^{[1
]}

Gorchinskiy, S. O. ^{[2
,3
]}

机构：

[1] Moscow MV Lomonosov State Univ, Fac Mech & Math, Moscow, Russia

[2] VA Steklov Math Inst, Moscow 117333, Russia

[3] Natl Res Univ, Higher Sch Econ, Moscow, Russia

来源：

SBORNIK MATHEMATICS | 2016年 / 207卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

finitely generated nilpotent groups; monomial representations; finite weight representations;

D O I：

10.1070/SM8582

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that irreducible complex representations of finitely generated nilpotent groups are monomial if and only if they have finite weight, which was conjectured by Parshin. Note that we consider (possibly infinite-dimensional) representations without any topological structure. In addition, we prove that for certain induced representations, irreducibility is implied by Schur irreducibility. Both results are obtained in a more general form for representations over an arbitrary field.

引用

页码：41 / 64

页数：24

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