Freudenthal-type multiplicity formulas for generalized Kac-Moody superalgebras

Abstract

In this paper we show that the Peterson root multiplicity formula and the Freudenthal weight multiplicity formula can be extended to the case of generalized Kac-Moody superalgebras. Applying these to some modular functions, we derive interesting relations among the Fourier coefficients. In particular, it will be shown that the Fourier coefficients of the elliptic modular function j - 744 can be determined only by the first three ones.