Vertex operator algebras, generalized doubles and dual pairs

By C. Dong, G. Yamskulna. 2000

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Abstract. Let V be a simple vertex operator algebra and G a finite automorphism group. Then there is a natural right G-action on the set of all inequivalent irreducible V-modules. Let ${\cal S}$ be a finite set of inequivalent irreducible V-modules which is closed under the action of G. There is a finite dimensional semisimple associative algebra $A_{\alpha}(G,{\cal S})$ for a suitable 2-cocycle $\alpha$ naturally determined by the G-action on ${\cal S}$ such that $A_{\alpha}(G,{\cal S})$ and the vertex operator algebra $V^G$ form a dual pair on the sum of V-modules in ${\cal S}$ in the sense of Howe. In particular, every irreducible V-module is completely reducible $V^G$-module.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fb482e4b6f74e65fef63a09b2ea52c3800d06786

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Citations in the corpus

On $G$--equivariant modular categories (2004, background): “ other terminology, the chiral algebra). In this case, we can form “quotient” theory which is described by the subalgebra of invariants VG ⊂V. These theories have been studied in numerous papers; see [DY] for references. Vertex operator algebras are complicated objects, and working with them is not ”
Modular Categories and Orbifold Models (2001, background): “X = L Xg. Then L ⊂ G(X) = Φ(IndX) (see (4.2)), which shows that L ∈ C′. Replacing RepA by Rep0A we get part (2) of the theorem. 4.3. Remark. This theorem contains as a special case the main result of [DY], which in our notation reads as follows: C 1 is equivalent to (Rep 0A)G as an abelian category.”