Compact automorphism groups of vertex operator algebras
Abstract
Let
V
be a simple vertex operator algebra which admits the continuous, faithful action of a compact Lie group
G
of automorphisms. We establish a Schur-Weyl type duality between the unitary, irreducible modules for
G
and the irreducible modules for
V
G
which are contained in
V
where
V
G
is the space of
G
-invariants of
V.
We also prove a concomitant Galois correspondence between vertex operator subalgebras of
V
which contain
V
G
and closed Lie subgroups of
G
in the case that
G
is abelian.