  Vogan raised the idea of Dirac cohomology to study representations of
semisimple Lie groups and Lie algebras. He conjectured that the infinitesimal
character of Harish-Chandra modules are determined by their Dirac cohomology.
Huang and Pand\v{z}i\'{c} proved this conjecture and initiated the research on
Dirac cohomology for Lie superalgebras based on Kostant's results. The aim of
the present paper is to study Dirac cohomology of unitary representations for
the general linear superalgebra and its relation to nilpotent Lie superalgebra
cohomology.
