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Journal of Lie Theory 29 (2019), No. 4, 1103--1118
Copyright Heldermann Verlag 2019

Translation of Dolbeault Representations

Nicolas Prudhon
Université de Lorraine, Institut Elie Cartan, UMR 7502 - CNRS, France

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.

Keywords: Dolbeault representations, cohomological induction, Zuckerman translation functors.

MSC: 22E46, 17B10.

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