Clifford algebra analogue of Cartan's theorem for symmetric pairs

2025/04/29 by Kieran Calvert, Calvert, Kieran, Karmen Grizelj +5
Mathematics · #17B20 #22E60 #57R91 #57T15 #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2504.20917

openalex publication_date 2025/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend Kostant's results about \mathfrakg-invariants in the Clifford algebra Cl(\mathfrakg) of a complex semisimple Lie algebra \mathfrakg to the relative case of \mathfrakk-invariants in the Clifford algebra Cl(\mathfrakp), where (\mathfrakg,\mathfrakk) is a classical symmetric pair and \mathfrakp is the (-1)-eigenspace of the corresponding involution. In this setup we prove the Cartan theorem for Clifford algebras, a relative transgression theorem, the Harish--Chandra isomorphism for Cl(\mathfrakp), and a relative version of Kostant's Clifford algebra conjecture.

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