Journal of Lie Theory

no. 4
Cubic Dirac Cohomology for Generalized Enright-Varadarajan Modules
Salah Mehdi1; Rajagopalan Parthasarathy2
1Dép. de Mathématiques, UMR 7122 - CNRS, Université Paul Verlaine, 57045 Metz, France
2Dept. of Mathematics, Bharathiar University, Coimbatore - 641 046, Tamil Nadu, India
Journal of Lie Theory, Volume 21 (2011) no. 4, pp. 861-884
\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.
DOI: 10.5802/jolt.653
Classification: 22E46, 22E47, 17B10
Keywords: Quadratic subalgebra, generalized Enright-Varadrajan module, (g,h)-module, Verma modules, Kostant's cubic Dirac operator, Dirac cohomology

Salah Mehdi  1 ; Rajagopalan Parthasarathy  2

1 Dép. de Mathématiques, UMR 7122 - CNRS, Université Paul Verlaine, 57045 Metz, France
2 Dept. of Mathematics, Bharathiar University, Coimbatore - 641 046, Tamil Nadu, India 
Salah Mehdi; Rajagopalan Parthasarathy. Cubic Dirac Cohomology for Generalized Enright-Varadarajan Modules. Journal of Lie Theory, Volume 21 (2011) no. 4, pp. 861-884. doi: 10.5802/jolt.653
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     title = {Cubic {Dirac} {Cohomology} for {Generalized} {Enright-Varadarajan} {Modules}},
     journal = {Journal of Lie Theory},
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     year = {2011},
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