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

Abstract

We classify all simple unitarizable supermodules over special linear Lie superalgebras using the algebraic Dirac operator introduced by Huang and Pandžić and the associated Dirac inequalities. The same argument treats finite-dimensional and infinite-dimensional supermodules without requiring explicit realizations or complete branching rules.

arXiv commentv2: Reorganized presentation and simplified proofs; 39 pages