Geodesic
Translation of Dolbeault Representations
Journal of Lie theory, Tome 29 (2019) no. 4, pp. 1103-1118
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We adapt techniques used in the study of the cubic Dirac operator on homogeneous reductive spaces to Dolbeault operators on elliptic coadjoint orbits. We reprove that cohomologically induced representations have an infinitesimal character, that cohomological induction and Zuckerman translation functor commute and we give a geometric interpretation of the Zuckerman translation functor for cohomologically induced representations.
Classification : 22E46, 17B10
Mots-clés : Dolbeault representations, cohomological induction, Zuckerman translation functors 
@article{JLT_2019_29_4_JLT_2019_29_4_a12,
     author = {N. Prudhon},
     title = {Translation of {Dolbeault} {Representations}},
     journal = {Journal of Lie theory},
     pages = {1103--1118},
     year = {2019},
     volume = {29},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2019_29_4_JLT_2019_29_4_a12/}
}
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N. Prudhon. Translation of Dolbeault Representations. Journal of Lie theory, Tome 29 (2019) no. 4, pp. 1103-1118. http://geodesic.mathdoc.fr/item/JLT_2019_29_4_JLT_2019_29_4_a12/