# The Super Orbit Challenge

## TL;DR

The paper introduces a new definition of super unitary representations for super Lie groups, ensuring all regular representations are super unitary, and explores a super orbit method for a specific Heisenberg-type super Lie group.

## Contribution

It proposes a novel definition of super unitary representations and applies a super orbit method to classify representations of a particular super Lie group.

## Key findings

- New super unitary representation definition ensures all regular representations are super unitary.
- List of super unitary representations for a Heisenberg-type super Lie group obtained via a heuristic super orbit method.
- Open challenge to develop a super orbit method that aligns with the proposed representations.

## Abstract

When using the generally adopted definition of a super unitary representation, there are lots of super Lie groups for which the regular representation is not super unitary. I propose a new definition of a super unitary representation for which all regular representations are super unitary. I then choose a particular super Lie group (of Heisenberg type) for which I provide a list of super unitary representations in my new sense, obtained by a heuristic super orbit method. The super orbit challenge is to find a well defined {super orbit method} that will reproduces more or less my list of super unitary representations (or explains why they should not appear).