Dirac cohomology and Θ-correspondence for complex dual pairs

2023/07/25 by Spyridon Afentoulidis-Almpanis, Gang Liu, Afentoulidis-Almpanis, Spyridon +3
Mathematics · #20G05 (Primary) 11F27 17B10 (Secondary) #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2307.13742

openalex publication_date 2023/07/25 · openalex created_date 2023/07/28 · openalex updated_date 2026/07/28

Abstract

We study the behavior of Dirac cohomology under Howe's Θ-correspondence in the case of complex reductive dual pairs. More precisely, if (G₁,G₂) is a complex reductive dual pair with G₁ and G₂ viewed as real groups, we describe those Harish-Chandra modules π₁ of G₁ with nonzero Dirac cohomology whose Θ-liftings Θ(π₁) still have nonzero Dirac cohomology. In this case, we compute explicitly the Dirac cohomology of Θ(π₁).

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