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, Tome 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.
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, Tome 21 (2011) no. 4, pp. 861-884. http://geodesic.mathdoc.fr/item/JOLT_2011_21_4_a6/
@article{JOLT_2011_21_4_a6,
author = {Salah Mehdi and Rajagopalan 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/JOLT_2011_21_4_a6/}
}
TY - JOUR
AU - Salah Mehdi
AU - Rajagopalan Parthasarathy
TI - Cubic Dirac Cohomology for Generalized Enright-Varadarajan Modules
JO - Journal of Lie Theory
PY - 2011
SP - 861
EP - 884
VL - 21
IS - 4
UR - http://geodesic.mathdoc.fr/item/JOLT_2011_21_4_a6/
ID - JOLT_2011_21_4_a6
ER -
%0 Journal Article
%A Salah Mehdi
%A Rajagopalan Parthasarathy
%T Cubic Dirac Cohomology for Generalized Enright-Varadarajan Modules
%J Journal of Lie Theory
%D 2011
%P 861-884
%V 21
%N 4
%U http://geodesic.mathdoc.fr/item/JOLT_2011_21_4_a6/
%F JOLT_2011_21_4_a6
