Dirac operators for Cartan motion groups

Spyridon Afentoulidis-Almpanis; Eyal Subag

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arXiv · 2609.37245

Dirac operators for Cartan motion groups

Spyridon Afentoulidis-Almpanis·Eyal Subag

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Abstract

We introduce and study the algebraic Dirac operator for the Cartan motion group associated with a real reductive Lie group. We establish its fundamental properties, including a square formula involving a natural Casimir-type element, define the corresponding notion of Dirac cohomology, and prove a strong form of Vogan's conjecture: a module in the Dirac series is completely determined by its Dirac cohomology. We explicitly determine the Dirac series of a Cartan motion group. We explain how the Dirac theory of a Cartan motion group can be obtained as the zero fiber of the recently introduced Dirac theory for the algebraic deformation family of the corresponding real reductive group.

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BibTeX RIS

Spyridon Afentoulidis-Almpanis, Eyal Subag. 2026-09-29. Dirac operators for Cartan motion groups. https://arxiv.org/abs/2609.37245

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