The simplicity of Kac modules for the quantum superalgebra U_q(gl(m,n))

TL;DR

This paper investigates the conditions under which Kac modules for the quantum superalgebra U_q(gl(m,n)) are simple and explores their relationship with representations of the even subalgebra U_q(g_{ ext{0}}).

Contribution

It provides new criteria for the simplicity of Kac modules and clarifies their connection to representations of the associated quantum subalgebra.

Findings

Criteria for simplicity of Kac modules established

Relationship between U_q(gl(m,n)) and U_q(g_{ ext{0}}) representations clarified

Enhanced understanding of quantum superalgebra module structure

Abstract

The simplicity of the Kac modules for the quantum superalgebra U_q(gl(m,n)) is studied, and the relation between the representation of U_q(gl(m,n)) and that of U_q(g_{\0}) is investigated.