Unitarity of minimal W-algebras and their representations II: Ramond sector

2024/05/29 by Victor G. Kač, Kac, Victor G., Pierluigi Möseneder Frajria +3 · 3 citations
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2405.19090

openalex publication_date 2024/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study unitary Ramond twisted representations of minimal W-algebras. We classify all such irreducible highest weight representations with a non-Ramond extremal highest weight (unitarity in the Ramond extremal case, as well as in the untwisted extremal case, remains open). We compute the characters of these representations and deduce from them the denominator identities for all superconformal algebras in the Neveu-Schwarz and Ramond sector. Some of the results rely on conjectures about the properties of the quantum Hamiltonian reduction functor in the Ramond sector.

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