Dirac series for complex classical Lie groups: A multiplicity-one theorem

2020/10/04 by Dan Barbasch, Chao-Ping Dong, Barbasch, Dan +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2010.01584

openalex publication_date 2020/10/04 · openalex created_date 2022/09/13 · openalex updated_date 2026/07/28

Abstract

This paper computes the Dirac cohomology H_D(π) of irreducible unitary Harish-Chandra modules π of complex classical groups viewed as real reductive groups. More precisely, unitary representations with nonzero Dirac cohomology are shown to be unitarily induced from unipotent representations. When nonzero, there is a unique, multiplicity free K-type in π contributing to H_D(π). This confirms conjectures formulated by the first named author and Pandzic in 2011.

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• Dirac operators for algebraic families

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