dorsal/arxiv
View SchemaCompact automorphism groups of vertex operator algebras
| Authors | Chongying Dong, Haisheng Li, Geoffrey Mason |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9608009 |
| URL | https://arxiv.org/abs/q-alg/9608009 |
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.
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"abstract": "Let $V$ be a simple vertex operator algebra which admits the continuous,\nfaithful action of a compact Lie group $G$ of automorphisms. We establish a\nSchur-Weyl type duality between the unitary, irreducible modules for $G$ and\nthe irreducible modules for $V^G$ which are contained in $V$ where $V^G$ is the\nspace of $G$-invariants of $V.$ We also prove a concomitant Galois\ncorrespondence between vertex operator subalgebras of $V$ which contain $V^G$\nand closed Lie subgroups of $G$ in the case that $G$ is abelian.",
"arxiv_id": "q-alg/9608009",
"authors": [
"Chongying Dong",
"Haisheng Li",
"Geoffrey Mason"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Compact automorphism groups of vertex operator algebras",
"url": "https://arxiv.org/abs/q-alg/9608009"
},
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