Using the notion of subprincipal symbol, we give a necessary condition for the existence of twisted D-modules simple along a smooth involutive submanifold of the cotangent bundle to a complex manifold. As an application, we prove that there are no generalized massless field equations with non-trivial twist on grassmannians, and in particular that the Penrose transform does not extend to the twisted case.
On twisted microdifferential modules I. Non-existence of twisted wave equations
Andrea D'Agnolo;
2004
Abstract
Using the notion of subprincipal symbol, we give a necessary condition for the existence of twisted D-modules simple along a smooth involutive submanifold of the cotangent bundle to a complex manifold. As an application, we prove that there are no generalized massless field equations with non-trivial twist on grassmannians, and in particular that the Penrose transform does not extend to the twisted case.
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