The regular representation, Zhu's $A(V)$-theory and induced modules

Abstract

The regular representation is related to Zhu's $A(V)$-theory and an induced module from an $A(V)$-module to a $V$-module is defined in terms of the regular representation. As an application, a new proof of Frenkel and Zhu's fusion rule theorem is obtained.

Latex, 30 pages; the final version to appear in Journal of Algebra