Duality of D-modules on flag manifolds (Q2708381)

Let \(\underline g\) be a complex semisimple Lie algebra with an involution \(\theta\), and let \(\underline h\) be the subalgebra of the fixed points of \(\theta\). Let \(H\) be a connected reductive algebraic group with \(\underline h\) as its Lie algebra. Let the adjoint action of \(\underline h\) on \(\underline g\) lift to an action of \(H\) on \(\underline g\). Let \(V\) be a Harish-Chandra module, i.e., \(V\) is a \((\underline g,H)\)-module such that any irreducible representation of \(H\) appears in \(V\) only finitely many times. The authors show that the characteristic variety of \(V^*\) is the complex conjugate of the characteristic variety of \(V\).