On monomial representations of finitely generated nilpotent groups. Issue 6 (3rd June 2018)

• Record Type: Journal Article
• Authors: Narayanan, E. K.; Singla, Pooja
• Is Part Of: Communications in algebra. Volume 46:Issue 6(2018)
• Page Start: 2319
• Page End: 2331
• Publication Date: 2018-06-03
• Subjects: Discrete Heisenberg groups -- finitely generated nilpotent groups -- induced representations -- monomial representations; Primary 20C15 -- Secondary 20F18 -- 22D30; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2017.1378894
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: A result of 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 Parshin, recently proved affirmatively by Beloshapka and Gorchinskii (2016), characterizes the monomial irreducible representations of finitely generated nilpotent groups. This article gives a slightly shorter proof of the conjecture using ideas of Kutzko and Brown. We also give a characterization of the finite-dimensional irreducible representations of two-step nilpotent groups and describe these completely for two-step groups whose center has rank one.