On the characters of a certain series of N=4 superconformal modules

In this paper we study the N=4 superconformal modules obtained from the quantum Hamiltonian reduction of principal admissible representations of the affine Lie superalgebra $\widehat{A}(1,1)$, and show that there exists a series of N=4 superconformal modules whose characters are modular functions and written explicitly by the Mumford’s theta functions.