On irreducible representations of discrete nilpotent groups

E. K. Narayanan, Pooja Singla

Published 2016-08-03Version 1

A conjecture of A. N. Parshin states that any countable dimensional irreducible representation of a finitely generated discrete nilpotent group is monomial. These are notes on the proof of the conjecture combining the ideas of I. D. Brown and P. C. Kutzko. This conjecture was recently proved by Beloshapka-Gorchinskii. We also provide a full description of the finite dimensional representations of two step groups whose center has rank one. At the end, we prove that a representations of two step nilpotent groups is finite dimensional if and only if its restriction to the commutator subgroup is direct sum of isotypic copies of a finite order character. Moreover in this case order of the obtained character of commutator subgroup divides the dimension of the irreducible representation.