Invariant formula of the determinant of a Heisenberg representation

TL;DR

This paper derives an explicit, choice-independent formula for the determinant of Heisenberg representations of finite groups, enhancing understanding of their algebraic structure.

Contribution

It provides a novel, explicit formula for the determinant of Heisenberg representations that does not depend on the induction method used.

Findings

Explicit formula for the determinant of Heisenberg representations

Independence from induction choices in the formula

Improved understanding of algebraic properties of Heisenberg representations

Abstract

In this paper we give an explicit formula of the determinant of a Heisenberg representation $\rho$ of a finite group $G$. Heisenberg representations are induced by 1-dimensional characters in multiple ways, but our formula will be independent of any particular choice of induction.