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

TL;DR

This paper establishes a Weyl-type character formula for a broad class of finite-dimensional simple modules over gl(m|n), called PDC modules, extending previous formulas to a larger module class.

Contribution

It proves a new character formula for PDC modules of gl(m|n), unifying and extending prior results for special cases.

Findings

Proves a character formula for PDC modules.

Includes totally connected and disconnected modules as special cases.

Advances the understanding of module characters in Lie superalgebras.

Abstract

In 1994, Kac and Wakimoto suggested a generalization of Bernstein and Leites character formula for basic Lie superalgebras, and the natural question was raised: to which simple highest weight modules does it apply? In this paper, we prove a similar formula for a large class of finite-dimensional simple modules over the Lie superalgebra gl(m|n), which we call piecewise disconnected modules, or PDC. The class of PDC modules naturally includes totally connected modules and totally disconnected modules, the two families for which similiar character formulas were proven by Su and Zhang as special cases of their general formula. This paper is part of our program for the pursuit of elegant character formulas for Lie superalgebras.