Dirac operators for algebraic families

2025/08/01 by Afentoulidis-Almpanis, Spyridon, Subag, Eyal
#14D99 (Secondary) #17B10 #17B20 #22E47 (Primary) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2508.00547

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.

Citations

• Dirac series for complex classical Lie groups: A multiplicity-one theorem
• The dependence on parameters of the inverse functor to the K-finite functor
• Dirac Index and associated cycles of Harish-Chandra modules
• Computing the associatied cycles of certain Harish-Chandra modules
• Mackey analogy as deformation of D-modules
• The algebraic Mackey-Higson bijections
• Contractions of Representations and Algebraic Families of Harish-Chandra Modules
• Algebraic Families of Harish-Chandra Pairs
• How tempered representations of a semisimple Lie group contract to its Cartan motion group
• Translation principle for Dirac index
• Higher Dirac cohomology of modules with generalized infinitesimal character
• Dirac cohomology of unipotent representations of Sp(2n,R) and U(p,q)
• Unitary representations of real reductive groups
• Dirac cohomology and unipotent representations of complex groups
• Dirac operators and Lie algebra cohomology

Related

• Algebraic Families of Harish-Chandra Pairs
• Two families of Dirac-like operators for Drinfeld's Hecke algebra
• Dirac operators and Lie algebra cohomology
• Dirac cohomology for the BGG category O
• Dirac cohomology for graded affine Hecke algebras