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In 1994, Kac and Wakimoto suggested a generalization of Bernstein and Leitescharacter formula for basic Lie superalgebras, and the natural question wasraised: to which simple highest weight modules does it apply? In this paper, weprove a similar formula for a large class of finite-dimensional simple modulesover the Lie superalgebra gl(m|n), which we call piecewise disconnectedmodules, or PDC. The class of PDC modules naturally includes totally connectedmodules and totally disconnected modules, the two families for which similiarcharacter formulas were proven by Su and Zhang as special cases of theirgeneral formula. This paper is part of our program for the pursuit of elegantcharacter formulas for Lie superalgebras.

A Weyl-Type character formula for PDC modules of gl(m|n)