Abstract
We study the representation theory for a class of so( N)-extended superconformal operator algebras, which was originally proposed by Knizhnik. Our main result is a set of conditions for consistency and unitarity, which are formulated in terms of the labels (Δ; m 1, m 2…, m [ N 2 ] ) that characterize an irreducible highest weight module. We exploit the correspondence of level-1 so( N)-extended superconformal theories, which have c N = 1 2 N + 1 , with certain free-field models, to derive character formulas for all representations that are allowed at level 1.
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