Journal of Lie Theory

no. 4
Translation of Dolbeault Representations
Journal of Lie Theory, Volume 29 (2019) no. 4, pp. 1103-1118
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.
DOI: 10.5802/jolt.1095
Classification: 22E46, 17B10
Keywords: Dolbeault representations, cohomological induction, Zuckerman translation functors 
@article{JOLT_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},
     doi = {10.5802/jolt.1095},
     zbl = {1442.22015},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1095/}
}
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N. Prudhon. Translation of Dolbeault Representations. Journal of Lie Theory, Volume 29 (2019) no. 4, pp. 1103-1118. doi: 10.5802/jolt.1095

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