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Journal of Lie Theory 27 (2017), No. 1, 111--121
Copyright Heldermann Verlag 2017

Dirac Operators and Cohomology for Lie Superalgebra of Type I

Wei Xiao
College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, Guangdong, P. R. China

D. Vogan jun. 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. J.-S. Huang and P. 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.

Keywords: Dirac cohomology, Lie superalgebra, Riemannian type, unitary representation.

MSC: 17B10

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