2013/07/27 by Chris Mauriello, Mauriello, Chris
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.1307.7324
119 pages
openalex publication_date 2013/07/27 · arxiv created 2013/07/28 · arxiv updated 2013/07/30 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
It is well known that using the weight lattice of type E6, P, and the lattice construction for vertex operator algebras one can obtain all three level 1 irreducible g-modules with VP = V\Lamba0 ⊕ V\Lamba1 ⊕ V\Lamba6. The Dynkin diagram of type E6 has an order 2 automorphism, τ, which can be lifted to τ, a Lie algebra automorphism of g of type E6^(1). The fixed points of τ are a subalgebra a of type F4^(1). The automorphism τ lifts further to τ a vertex operator algebra automorphism of VP. We investigate the branching rules, how these three modules for the affine Lie algebra g decompose as a direct sum of irreducible a-modules. To complete the decomposition we use the Godard-Kent-Olive coset construction which gives a c = (4)/(5) module for the Virasoro algebra on VP which commutes with a. We use the irreducible modules for this coset Virasoro to give the space of highest weight vectors for a in each V\Lambai. The character theory related to this decomposition is examined and we make a connection to one of the famous Ramanujan identities. This dissertation constructs coset Virasoro operators Y(\omg,z) by explicitly determining the generator \omg. We also give the explicit highest weight vectors for each Vir ⊗ F4^(1)-module in the decomposition of each V\Lambai. This explicit work on determining highest weight vectors gives some insight into the relationship to the Zamolodchikov W3-algebra.