Generalized Verma Modules and Character Formulae for $\mathfrak{osp}(3|2m)$

TL;DR

This paper derives explicit character formulas for all finite-dimensional irreducible modules of the Lie superalgebra fosp(3|2m), expressing them through generalized Verma modules, advancing understanding of superalgebra representations.

Contribution

It provides the first comprehensive character formula for fosp(3|2m) irreducible modules using generalized Verma modules, filling a key gap in superalgebra representation theory.

Findings

Explicit character formulas for fosp(3|2m) modules

Representation of characters via generalized Verma modules

Enhanced understanding of superalgebra module structures

Abstract

The character formula of any finite dimensional irreducible module for Lie superalgebra $\mathfrak{osp}(3|2m)$ is obtained in terms of characters of generalized Verma modules.