Modul:   MAT772  Geometrie-Seminar

Irreducible representations of finitely generated nilpotent groups: Parshin's conjecture

Talk by Dr. Iuliya Beloshapka

Date: 28.02.18  Time: 15.45 - 18.00  Room: ETH HG G 43

At ICM 2010 Parshin conjectured that irreducible complex representations of finitely generated nilpotent groups are monomial if and only if they have finite weight. This was previously known to be true for finite nilpotent groups and for unitary irreducible representations of connected nilpotent Lie groups (A.A. Kirillov and J. Dixmier). We prove Parshin's conjecture in full generality. We will also discuss how to approach moduli space problem for such representations since the question is related to higher-dimensional adeles, and it potentially has interesting geometry. For nilpotency classes 2 and 3 we obtained a full description.