Kostant's cubic Dirac operator of Lie Superalgebras

TL;DR

This paper extends the concept of equal rank embedding from reductive Lie algebras to basic Lie superalgebras, deriving character formulas and constructing a Kostant cubic Dirac operator that incorporates both even and odd generators.

Contribution

It introduces a new framework for equal rank embedding in Lie superalgebras and constructs a Kostant cubic Dirac operator tailored for these structures.

Findings

Derived Kac character formulas for Lie superalgebras

Constructed a Kostant cubic Dirac operator for superalgebras

Extended equal rank embedding theory to superalgebras

Abstract

We extend equal rank embedding of reductive Lie algebras to that of basic Lie superalgebras. The Kac character formulas for equal rank embedding are derived in terms of subalgebras and Kostant's cubic Dirac operator for equal rank embedding of Lie superalgebras is constructed from both even and odd generators and their related structure constants.