Dirac operators for algebraic families

Spyridon Afentoulidis-Almpanis; Eyal Subag

doi:10.1016/j.aim.2026.110973

Dirac operators for algebraic families

Spyridon Afentoulidis-Almpanis
, Eyal Subag

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	110973
Journal	Advances in Mathematics
Volume	496
DOIs	https://doi.org/10.1016/j.aim.2026.110973
State	Published - Jun 2026

Bibliographical note

Publisher Copyright:
© 2026 The Authors.

Keywords

Algebraic families
Dirac cohomology
Dirac operators
Harish-Chandra modules
Vogan's conjecture

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10.1016/j.aim.2026.110973

Cite this

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AB - 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.

KW - Algebraic families

KW - Dirac cohomology

KW - Dirac operators

KW - Harish-Chandra modules

KW - Vogan's conjecture

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Dirac operators for algebraic families

Abstract

Bibliographical note

Keywords

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