On the simplicity of Kac modules for the restricted Lie superalgebra gl(m,n)

TL;DR

This paper provides a characteristic-free criterion for the simplicity of Kac modules over the restricted Lie superalgebra gl(m,n), and explores its implications for nonrestricted representations.

Contribution

It introduces a complete, characteristic-free polynomial criterion for simplicity of Kac modules and applies it to nonrestricted representations.

Findings

Polynomial criterion fully determines simplicity of Kac modules

Application of criterion to nonrestricted representations

Advances understanding of representation theory for gl(m,n)

Abstract

The polynomial which determine the simplicity of the Kac modules for the restricted Lie superalgebra gl(m,n) is completely determined by a characteristic free approach. Its application on the nonrestricted representation is investigated.