Araki Cohomology of the de Sitter Scalar Discrete Series
Abstract
Building on the recently established de Sitter (dS)-covariant indecomposable Krein realization of the scalar discrete-series unitary irreducible representations Πp,0, p=1,2,⋯, of SO0(1,4), naturally organized into a Gupta-Bleuler triplet, we uncover its underlying Araki-cohomological structure. We show that the Krein-Gupta-Bleuler construction provides a concrete realization of Araki's standard Gupta-Bleuler triplet, with its non-split indecomposable structure encoded by non-trivial first cohomology classes related by adjunction. We further show that the reducible intermediate sector naturally resolves into its two irreducible components, inducing a corresponding decomposition of the extension classes and yielding a four-layer refinement of Araki's standard triplet. The resulting Gupta-Bleuler quadruplet provides a finer cohomological resolution, distinguishing the physical representation from its complex-conjugate sector.
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BibTeX
@misc{bajalan2026araki,
title = {{Araki Cohomology of the de Sitter Scalar Discrete Series}},
author = {Maryam Bajalan and Jean-Pierre Gazeau and Hamed Pejhan and Petr Siegl},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07090},
eprint = {2610.07090},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05829805v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Araki Cohomology of the de Sitter Scalar Discrete Series
AU - Maryam Bajalan
AU - Jean-Pierre Gazeau
AU - Hamed Pejhan
AU - Petr Siegl
PY - 2026
DA - 2026/10/05
PB - HAL
DO - 10.48550/arxiv.2610.07090
UR - https://hal.science/hal-05829805v1
AB - Building on the recently established de Sitter (dS)-covariant indecomposable Krein realization of the scalar discrete-series unitary irreducible representations Π_p,0, p=1,2,⋯, of SO_0(1,4), naturally organized into a Gupta-Bleuler triplet, we uncover its underlying Araki-cohomological structure. We show that the Krein-Gupta-Bleuler construction provides a concrete realization of Araki's standard Gupta-Bleuler triplet, with its non-split indecomposable structure encoded by non-trivial first cohomology classes related by adjunction. We further show that the reducible intermediate sector naturally resolves into its two irreducible components, inducing a corresponding decomposition of the extension classes and yielding a four-layer refinement of Araki's standard triplet. The resulting Gupta-Bleuler quadruplet provides a finer cohomological resolution, distinguishing the physical representation from its complex-conjugate sector.
ER -