On the full set of unitarizable supermodules over $\mathfrak{sl}(m\vert n)$

TL;DR

This paper introduces a new classification of unitarizable supermodules over re9sl(m|n) Lie superalgebras by employing an algebraic quadratic Dirac operator and a Dirac inequality, advancing the understanding of their structure.

Contribution

It provides a novel algebraic approach to classify unitarizable supermodules over re9sl(m|n) using Dirac operators, which was not previously established.

Findings

New classification scheme for unitarizable supermodules

Application of algebraic quadratic Dirac operator in supermodule analysis

Establishment of a Dirac inequality for supermodules

Abstract

We present a novel classification of unitarizable supermodules over special linear Lie superalgebras using an algebraic quadratic Dirac operator introduced by Huang and Pand\v{z}i\'c and a corresponding Dirac inequality.