On the representation theory of the vertex algebra L−5/2(sl(4))

Scientific paper - Original scientific paper

• Author: Dražen Adamović
• Author: Ozren Perše
• Author: Ivana Vukorepa
• Author's institution: University of Zagreb; Faculty of Science; (Department of Mathematics)
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract (english)

We study the representation theory of non-admissible simple affine vertex algebra L−5/2(sl(4)). We determine an explicit formula for the singular vector of conformal weight four in the universal affine vertex algebra V−5/2(sl(4)), and show that it generates the maximal ideal in V−5/2(sl(4)). We classify irreducible L−5/2(sl(4))-modules in the category O, and determine the fusion rules between irreducible modules in the category of ordinary modules KL−5/2. It turns out that this fusion algebra is isomorphic to the fusion algebra of KL−1. We also prove that KL−5/2 is a semi-simple, rigid braided tensor category. In our proofs, we use the notion of collapsing level for the affine W-algebra, and the properties of conformal embedding gl(4)↪sl(5) at level k=−5/2 from D. Adamovic et al. [Finite vs infinite decompositions in conformal embeddings, Comm. Math. Phys. 348 (2016) 445–473.]. We show that k=−5/2 is a collapsing level with respect to the subregular nilpotent element fsubreg, meaning that the simple quotient of the affine W-algebra W−5/2(sl(4),fsubreg) is isomorphic to the Heisenberg vertex algebra MJ(1). We prove certain results on vanishing and non-vanishing of cohomology for the quantum Hamiltonian reduction functor Hfsubreg. It turns out that the properties of Hfsubreg are more subtle than in the case of minimal reduction.

• Keywords (english): affine vertex algebras; vertex operator algebras; fusion rules; conformal embeddings; representation theory
• Language: english
• Publication type: Scientific paper - Original scientific paper
• Publication status: Published
• Peer review: Peer review - international
• Publication version: Published version
• Journal title: Communications in Contemporary Mathematics
• Numbering: vol. 25, no. 2, 2150104
• p-ISSN: 0219-1997
• e-ISSN: 1793-6683
• DOI: https://doi.org/10.1142/S0219199721501042
• URN:NBN: urn:nbn:hr:217:622276
• Publication: 2023
• Project: Number: KK.01.1.1.01.0004; Title (english): QuantiXLie Center of Excellence; Leader: Marketin, Tomislav; Jurisdiction: eu; Funding stream: European Regional Development Fund - the Competitiveness and Cohesion Operational Programme
• Document URL: https://www.worldscientific.com/doi/10.1142/S0219199721501042
• Type of resource: Text
• Access conditions: Institutional access
• Created on: 2023-02-23 11:38:59