On Schur multiplier and projective representations of Heisenberg groups

TL;DR

This paper investigates the Schur multiplier and projective representations of discrete and finite Heisenberg groups, providing explicit constructions of their representation groups and irreducible projective representations.

Contribution

It offers a detailed analysis of the Schur multiplier for Heisenberg groups and constructs their finite-dimensional projective irreducible representations.

Findings

Schur multiplier computed for various Heisenberg groups

Explicit construction of representation groups provided

Finite-dimensional projective irreducible representations characterized

Abstract

In this article, we study the Schur mutiplier of the discrete as well as the finite Heisenberg groups and their t-variants. We describe the representation groups of these Heisenberg groups and through these give a construction of their finite dimensional complex projective irreducible representations.