Rationality of quotients by finite Heisenberg groups

TL;DR

This paper proves that the quotient of complex n-space by the finite Heisenberg group acting through its irreducible representation is always rational for all positive integers n.

Contribution

It establishes the rationality of quotients by finite Heisenberg groups acting on complex vector spaces, a result previously unknown for all dimensions.

Findings

The quotient ^n / H_n is rational for all n .

The proof applies to any dimension n, extending known results.

The result advances understanding of quotient spaces under finite group actions.

Abstract

We prove rationality of the quotient $\mathbb{C}^n / H_n$ for the finite Heisenberg group $H_n$, any $n \ge 1$, acting on $\mathbb{C}^n$ via its irreducible representation.