Geodesic
Dirac Operators and Cohomology for Lie Superalgebra of Type I
Wei Xiao1
1College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, Guangdong, P. R. China
Journal of Lie Theory, Tome 27 (2017) no. 1, pp. 111-121

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 17B10
Mots-clés : Dirac cohomology, Lie superalgebra, Riemannian type, unitary representation

Wei Xiao  1

1 College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, Guangdong, P. R. China 
Wei Xiao. Dirac Operators and Cohomology for Lie Superalgebra of Type I. Journal of Lie Theory, Tome 27 (2017) no. 1, pp. 111-121. http://geodesic.mathdoc.fr/item/JOLT_2017_27_1_a4/
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     author = {Wei Xiao},
     title = {Dirac {Operators} and {Cohomology} for {Lie} {Superalgebra} of {Type} {I}},
     journal = {Journal of Lie Theory},
     pages = {111--121},
     year = {2017},
     volume = {27},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2017_27_1_a4/}
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