Unitarity of minimal $W$-algebras and their representations I

TL;DR

This paper systematically studies the unitarity of minimal W-algebras, classifies their unitary forms and irreducible modules, and computes their characters, advancing understanding of their representation theory.

Contribution

It provides a classification of unitary minimal W-algebras and their irreducible highest weight modules, along with character formulas, which is a significant step forward in the field.

Findings

Classified all unitary minimal W-algebras.

Progressed in classifying their unitary irreducible modules.

Computed characters of these modules.

Abstract

We begin a systematic study of unitary representations of minimal $W$-algebras. In particular, we classify unitary minimal $W$-algebras and make substantial progress in classification of their unitary irreducible highest weight modules. We also compute the characters of these modules.