Geodesic
Cubic Dirac Cohomology for Generalized Enright-Varadarajan Modules
Journal of Lie theory, Tome 21 (2011) no. 4, pp. 861-884
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\def\g{{\frak g}} \def\h{{\frak h}} \def\v{{\frak v}} For a complex semisimple Lie algebra $\g=\h\oplus\v$ where $\h$ is a quadratic subalgebra and $\h$ and $\v$ are orthogonal with respect to the Killing form, we construct a large family of $(\g,\h)$-modules with non-zero cubic Dirac cohomology. Our method uses analogue of the construction of generalized Enright-Varadarajan modules for what we call $(\h,\v)$-split parabolic subalgebras. This family of modules includes discrete series representations and ${\cal A}_{\q}(\lambda)$-modules.
Classification : 22E46, 22E47, 17B10
Mots-clés : Quadratic subalgebra, generalized Enright-Varadrajan module, (g,h)-module, Verma modules, Kostant's cubic Dirac operator, Dirac cohomology 
@article{JLT_2011_21_4_JLT_2011_21_4_a6,
     author = {S. Mehdi and R. Parthasarathy},
     title = {Cubic {Dirac} {Cohomology} for {Generalized} {Enright-Varadarajan} {Modules}},
     journal = {Journal of Lie theory},
     pages = {861--884},
     year = {2011},
     volume = {21},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2011_21_4_JLT_2011_21_4_a6/}
}
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S. Mehdi; R. Parthasarathy. Cubic Dirac Cohomology for Generalized Enright-Varadarajan Modules. Journal of Lie theory, Tome 21 (2011) no. 4, pp. 861-884. http://geodesic.mathdoc.fr/item/JLT_2011_21_4_JLT_2011_21_4_a6/