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Characters and relations among <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mi mathvariant="script">S</mml:mi><mml:mi mathvariant="script">W</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>3</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> algebras
The $\mathcal{S}\mathcal{W}(3/2,2)$ current algebras come in two discrete series indexed by central charge, with the chiral algebra of a supersymmetric sigma model on a Spin(7) manifold as a special case. The unitary representations of these algebras were classified by Gepner and Noyvert, and we use their results to perform an …