Nakano, Hiromu, Hunziker, Florencia Orosz, Camacho, Ana Ros and Wood, Simon  ORCID: https://orcid.org/0000-0002-8257-0378
2026.
Fusion rules and rigidity for weight modules over the simple admissible affine sl(2) and N=2 superconformal vertex operator superalgebras.
Advances in Mathematics
502
(Part A)
, 111124.
10.1016/j.aim.2026.111124
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Abstract
We prove that the categories of weight modules over the simple Image 1 and superconformal vertex operator superalgebras at fractional admissible levels and central charges are rigid (and hence the categories of weight modules are braided ribbon categories) and that the decomposition formulae of fusion products of simple projective modules conjectured by Thomas Creutzig, David Ridout and collaborators hold (including when the decomposition involves summands that are indecomposable yet not simple). In addition to solving this old open problem, we develop new techniques for the construction of intertwining operators by means of integrating screening currents over certain cycles, which are expected to be of independent interest, due to their applicability to many other algebras. In the example of Image 2 these new techniques allow us to give explicit formulae for a logarithmic intertwining operator from a pair of simple projective modules to the projective cover of the tensor unit, namely, the vertex operator algebra as a module over itself.
| Item Type: | Article |
|---|---|
| Date Type: | Publication |
| Status: | Published |
| Schools: | Schools > Mathematics |
| Additional Information: | RRS applied |
| Publisher: | Elsevier |
| ISSN: | 0001-8708 |
| Date of First Compliant Deposit: | 14 July 2026 |
| Date of Acceptance: | 24 June 2026 |
| Last Modified: | 14 Jul 2026 15:30 |
| URI: | https://orca.cardiff.ac.uk/id/eprint/188181 |
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