Irreducible modules L(c_p,q,h_m,n) over Vir_p,q are classically free precisely for boundary minimal models Vir_{2,2s+1}, with classical limits described by jet algebras of the corresponding Zhu C2-algebras, thereby interpreting the Andrews-Gordon identities.
Introduction to Vertex Algebras
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abstract
These lecture notes are intended to give a modest impulse to anyone willing to start or pursue a journey into the theory of Vertex Algebras by reading one of Kac's or Lepowsky-Li's books. Therefore, the primary goal is to provide required tools and help being acquainted with the machinery which the whole theory is based on. The exposition follows Kac's approach. Fundamental examples relevant in Theoretical Physics are also discussed. No particular prerequisites are assumed.
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Boundary minimal models and the Rogers-Ramanujan identities
Irreducible modules L(c_p,q,h_m,n) over Vir_p,q are classically free precisely for boundary minimal models Vir_{2,2s+1}, with classical limits described by jet algebras of the corresponding Zhu C2-algebras, thereby interpreting the Andrews-Gordon identities.