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

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.

Latex file, 60 pages. arXiv admin note: text overlap with arXiv:2012.14643; minor changes in the Introduction

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