Vertex operator algebras associated to admissible representations of ŝl2

Chongying Dong, Haisheng Li, Geoffrey Mason

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


The Kac-Wakimoto admissible modules for ŝl2 are studied from the point of view of vertex operator algebras. It is shown that the vertex operator algebra L(l, 0) associated to irreducible highest weight modules at admissible level l = p/q - 2 is not rational if l is not a positive integer. However, a suitable change of the Virasoro algebra makes L(l, 0) a rational vertex operator algebra whose irreducible modules are exactly these admissible modules for ŝl2 and for which the fusion rules are calculated. It is also shown that the q-dimensions with respect to the new Virasoro algebra are modular functions.

Original languageEnglish (US)
Pages (from-to)65-93
Number of pages29
JournalCommunications In Mathematical Physics
Issue number1
StatePublished - 1997
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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