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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.
akable@math.okstate.edu



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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