Abstract
Possible unitary statistical models and SU(2) current algebra theories are classified up to certain “levels” of the Virasoro and Kac-Moody algebras. A connection that is found between the Virasoro and SU(2) Kac-Moody characters is used to generate unitary statistical models from the SU(2) theories. Using the “fusion rules” of the operator product algebra of these theories, we are able to check the consistency of the solutions, and to write down their operator product algebra. The connection between the two algebras extends also to the fusion rules.
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