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Peer-reviewedCC BY 4.0Journal of Lie Theory

Translation of Dolbeault Representations

  • Nicolas Prudhon
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Abstract

We adapt techniques used in the study of the cubic Dirac operator on homogeneous reductive spaces to Dolbeault operators on elliptic coadjoint orbits. We prove 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 .

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Cite

BibTeXRIS
BibTeX
@article{prudhon2026translation,
  title = {{Translation of Dolbeault Representations}},
  author = {Nicolas Prudhon},
  journal = {Journal of Lie Theory},
  year = {2026},
  month = oct,
  doi = {10.5802/jolt.1095},
  url = {https://hal.science/hal-05781989v1},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Translation of Dolbeault Representations
AU  - Nicolas Prudhon
PY  - 2026
DA  - 2026/10/06
JO  - Journal of Lie Theory
DO  - 10.5802/jolt.1095
UR  - https://hal.science/hal-05781989v1
AB  - We adapt techniques used in the study of the cubic Dirac operator on homogeneous reductive spaces to Dolbeault operators on elliptic coadjoint orbits. We prove 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 .
SN  - 0949-5932
ER  -