##
Vertex operator algebras and dual pairs

**Gaywalee Yamskulna**,

University of California at Santa Cruz
Let V be a simple vertex operator algebra and G a finite automorphism

group of V. A major problem in orbifold conformal field theory is to

determine the module category of V^G. Here V^G is the G-invariant

sub-vertex operator algebra of V. Let S be a finite set of

inequivalent irreducible V-modules. Then there is a finite dimensional

semisimple associative algebra A_{\lapha}(G,S) such that A_{\alpha}(G,S)

and V^G form a dual pair on the sum of V_modules in S in the sense
of

Howe. In particular, every irreducible V-module is completely reducible

V^G-module.