Dirac operators for algebraic families
Representation Theory
2026-05-12 v2 Rings and Algebras
Abstract
We introduce algebraic families of Dirac operators for the deformation family (and other related families) associated with a real reductive Lie group that interpolates the reductive group and the corresponding Cartan motion group. We prove Vogan's conjecture in this setting, relating the infinitesimal character of an algebraic family of Harish-Chandra modules and its Dirac cohomology.
Cite
@article{arxiv.2508.00547,
title = {Dirac operators for algebraic families},
author = {Spyridon Afentoulidis-Almpanis and Eyal Subag},
journal= {arXiv preprint arXiv:2508.00547},
year = {2026}
}
Comments
correction of typos, revised version following referee comments, 61 pages