Determinant representations for Garvan formulas

Abstract

In this note, we demonstrate how determinant representations for correlation functions in conformal field theory can be used to derive explicit determinant formulas for powers of the classical $\hat{I}\cdot$-function, expressed via deformed elliptic functions with parameters. In particular, we obtain counterparts of Garvan's formulas for the modular discriminant corresponding to the genus two Riemann surface case.