Study on representations of conformal suepralgebras and applications to mathematical physics Study on representations of conformal suepralgebras and applications to mathematical physics

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In this research, we obtained the following results concerning conformal superalgebras:1. The Virasoro algebra is contained in conformal superalgebras as a subalgebra, and it plays important roles in the representation theory of conformal superalgebras. We publish a book correcting basic results in the representation theory of the Virasoro algebra in collaboration with K. Iohara (Lyon Univ.).2. A close relation between a conformal and a Kac-Moody superalgebras is known. We study the singular vector formula for some Kac-Moody superalgebras.