Rationality of admissible affine vertex algebras in the category O
By T. Arakawa. 2012
109 citations recorded by the source corpus.
We study the vertex algebras associated with modular invariant representations of affine Kac-Moody algebras at fractional levels, whose simple highest weight modules are classified by Joseph's characteristic varieties. We show that an irreducible highest weight representation of a non-twisted affine Kac-Moody algebra at an admissible level k is a module over the associated simple affine vertex algebra if and only if it is an admissible representation whose integral root system is isomorphic to that of the vertex algebra itself. This in particular proves the conjecture of Adamovic and Milas on the rationality of admissible affine vertex algebras in the category O.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/ae7f3f7608e47e5b9712a329725e36817a9e2c05
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In Algebra and Number Theory
In Geometry and Topology
In Statistical and Nonlinear Physics
Citations in the corpus
- Rationality of W-algebras: principal nilpotent cases (2012, methodology): “We deduce the classification result in the Main Theorem from that of admissible affine vertex algebras L ( k Λ 0 ) recently obtained by the author in [Ara12a].”
- Fusion categories for affine vertex algebras at admissible levels (2018, background): “Tomoyuki Arakawa has proven that this category is semi-simple [14] and so it is natural to wonder if this category is even a ribbon or modular tensor category.”