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Paper IPM / Physic / 7931  


Abstract:  
Recently, conformal algebras with extended wupersymmetry have attracted a lot of attention. These algebras have a basic importance in analysis of algebraic structure of varieties of string theories and are also relevant to the description of critical properties of some statistical models. The character formula for some of unitary representation in case of N=4 have been derived long time ago, and shown that there are two representations which are massive and massless for R and NS sector. The partition function from N=4 algebra has a connection with sl(21;C) subalgebra of D(21;α). So in this talk, we investigate the representation of N=4 and D(21;α) and also we show that they have deep relation to zeto mode. In order to relate the representation algebras, we must first obtain the generators of D(21;α) in general mode, and then compare with N=4 superconformal algebra in zero mode. We also discuss the character formula in these two algebras.
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