Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Institution: Bar-Ilan University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214952881