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Journal of Lie Theory 28 (2018), No. 4, 969--985
Copyright Heldermann Verlag 2018

A Note on the Construction of Second-Order Conformally Invariant Systems on Generalized Flag Manifolds

Anthony C. Kable
Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, U.S.A.

An automatic conformal invariance result is proved for systems of second-order differential operators on generalized flag manifolds. The result states that a purely algebraic datum (analogous to the symbol of a differential operator) that has the correct shape to have arisen from a conformally invariant system of second-order operators on a homogeneous line bundle does, in fact, arise from such a system on a suitable bundle.

Keywords: Graded Lie algebra, generalized Verma module.

MSC: 17B10; 22E47, 35R03

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