$Q$-representations and unitary representations of the super-Heisenberg group and harmonic superanalysis

TL;DR

This paper compares two approaches to representing the super-Heisenberg group, focusing on harmonic superanalysis and the strict theory of unitary representations, advancing understanding of super Lie group representations.

Contribution

It introduces a unified perspective by juxtaposing the physical and mathematical approaches to super-Heisenberg group representations, highlighting their connections and differences.

Findings

Harmonic superanalysis provides a concrete framework for super-group analysis.

The strict theory offers a rigorous classification of unitary super-representations.

The paper bridges physical intuition with mathematical formalism in supergroup representations.

Abstract

We juxtapose two approaches to the representations of the super-Heisenberg group. Physical one, sometimes called concrete approach, based on the super-wave functions depending on the anti-commuting variables, yielding the harmonic superanalysis and recently developed strict theory of unitary representations of the nilpotent super Lie groups covering the unitary representations of the super-Heisenberg group.