On quantum Galois theory
Abstract
For a simple vertex operator algebra $V$ and a finite automorphism group $G$ of $V$ then $V$ is a direct sum of $V^{\chi}$ where $\chi$ are irreducible character of $G$ and $V^{\chi}$ is the subspace of $V$ which $G$ acts according to the character $\chi.$ We prove the following: 1. Each $V^{\chi}$ is nonzero. 2. $V^{\chi}$ is a tensor product $M_{\chi}\otimes V_{\chi}$ where $M_{\chi}$ is an irreducible $G$module affording $\chi$ and $V_{\chi}$ is a $V^G$module. If $G$ is solvable, $V_{\chi}$ is a simple $V^G$module and $M_{\chi}\mapsto $V_{\chi}$ is a bijection from the set of irreducible $G$modules to the set of (inequivalent) simple $V^G$modules which are contained in $V.$
 Publication:

arXiv eprints
 Pub Date:
 December 1994
 arXiv:
 arXiv:hepth/9412037
 Bibcode:
 1994hep.th...12037D
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Quantum Algebra
 EPrint:
 25 pages, latex, no figures