Vertex Operator Algebras Associated to Type G Affine Lie Algebras II

2011/12/29 by Jonathan C. Axtell, Jonathan Axtell, Axtell, Jonathan
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.1112.6289

28 pages, 1 table

arxiv created 2011/12/29 · openalex publication_date 2011/12/29 · arxiv updated 2011/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We continue the study of the vertex operator algebra L(k,0) associated to a type G₂⁽¹⁾ affine Lie algebra at admissible one-third integer levels, k = -2 + m + \tfraci3 (m∈ ℤ_{≥ 0}, i = 1,2), initiated in \citeAL. Our main result is that there is a finite number of irreducible L(k,0)-modules from the category O. The proof relies on the knowledge of an explicit formula for the singular vectors. After obtaining this formula, we are able to show that there are only finitely many irreducible A(L(k,0))-modules form the category O. The main result then follows from the bijective correspondence in A(V)-theory.

Related

• Vertex Operator Algebras Associated to Type G Affine Lie Algebras
• A note on representations of some affine vertex algebras of type D
• A construction of admissible A₁⁽¹⁾-modules of level -4/3
• A construction of some ideals in affine vertex algebras
• Vertex operator algebras associated to modified regular representations of affine Lie algebras