Dirac Operators and Cohomology for Lie Superalgebra of Type I

摘要

Vogan raised the idea of Dirac cohomology to study representations of semisimple Lie groups and Lie algebras. He conjectured that the infinitesimal characters of Harish-Chandra modules are determined by their Dirac cohomology. Huang and Pandzic 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 basic classical Lie superalgebra of Type I and its relation to nilpotent Lie superalgebra cohomology.