A System of Third-Order Differential Operators Conformally Invariant under \mathfrakso(8,ℂ)

2010/11/03 by Toshihisa Kubo, Kubo, Toshihisa
Mathematics · #17B10 #22E46 #22E47 #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.1011.0963

openalex publication_date 2010/11/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In earlier work, Barchini, Kable, and Zierau constructed a number of conformally invariant systems of differential operators associated to Heisenberg parabolic subalgebras in simple Lie algebras. The construction was systematic, but the existence of such a system was left open in several anomalous cases. Here, a conformally invariant system is shown to exist in the most interesting of these remaining cases. The construction may also be interpreted as giving an explicit homomorphism between generalized Verma modules for the Lie algebra of type D₄.

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